Research graph
References from From fractional Lane–Emden–Serrin equation—existence, multiplicity and local behaviors via classical ODE—to fractional Yamabe metrics with singularity of “maximal” dimension. Local targets link to admitted publications; unresolved targets remain external evidence.
Large 𝑆-harmonic functions and boundary blow-up solutions for the fractional Laplacian
10.3934/dcds.2015.35.5555 · 2015 · External reference
Unresolved reference
1964 · External reference
Existence of positive weak solutions for fractional Lane-Emden equations with prescribed singular sets
10.1007/s00526-018-1425-8 · 2018 · External reference
A gluing approach for the fractional Yamabe problem with isolated singularities
10.1515/crelle-2018-0032 · 2020 · External reference
On higher-dimensional singularities for the fractional Yamabe problem: a nonlocal Mazzeo-Pacard program
10.1215/00127094-2019-0034 · 2019 · External reference
ODE methods in non-local equations
10.4208/jms.v53n4.20.01 · 2020 · External reference
Fast and slow decay solutions for supercritical fractional elliptic problems in exterior domains
10.1017/prm.2020.91 · 2022 · External reference
Uniqueness for the nonlocal Liouville equation in ℝ
10.1016/j.jfa.2022.109712 · 2022 · External reference
On isolated singularities in some nonlinear partial differential equations
10.1512/iumj.1983.32.32051 · 1983 · External reference
Local behavior of solutions of some elliptic equations
10.1007/bf01210610 · 1987 · External reference
Isolated boundary singularities of semilinear elliptic equations
10.1007/s00526-010-0337-z · 2011 · External reference
Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations
10.1007/bf01243922 · 1991 · External reference
The sharp exponent in the study of the nonlocal Hénon equation in ℝ^{ℕ}: a Liouville theorem and an existence result
10.1007/s00526-020-01763-z · 2020 · External reference
10.1515/9783110269291
10.1515/9783110269291 · 2012 · External reference
Some observations on the Green function for the ball in the fractional Laplace framework
10.3934/cpaa.2016.15.657 · 2016 · External reference
Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth
10.1002/cpa.3160420304 · 1989 · External reference
An extension problem related to the fractional Laplacian
10.1080/03605300600987306 · 2007 · External reference
Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities
10.1007/s00205-014-0722-4 · 2014 · External reference
An analytic construction of singular solutions related to a critical Yamabe problem
10.1080/03605302.2020.1784209 · 2020 · External reference
Unresolved reference
External reference
Unresolved reference
1957 · External reference
Fractional Laplacian in conformal geometry
10.1016/j.aim.2010.07.016 · 2011 · External reference
Existence of positive weak solutions with a prescribed singular set of semilinear elliptic equations
10.1007/bf02921937 · 1999 · External reference
Unresolved reference
External reference
A direct method of moving planes for the fractional Laplacian
10.1016/j.aim.2016.11.038 · 2017 · External reference
Qualitative properties of solutions for an integral equation
10.3934/dcds.2005.12.347 · 2005 · External reference
Classification of solutions for an integral equation
10.1002/cpa.20116 · 2006 · External reference
Classification of isolated singularities of nonnegative solutions to fractional semi-linear elliptic equations and the existence results
10.1112/jlms.12104 · 2018 · External reference
Finite Morse index solutions of an elliptic equation with supercritical exponent
10.1016/j.jde.2011.02.005 · 2011 · External reference
Delaunay-type singular solutions for the fractional Yamabe problem
10.1007/s00208-016-1483-1 · 2017 · External reference
Isolated singularities for a semilinear equation for the fractional Laplacian arising in conformal geometry
10.4171/rmi/1038 · 2018 · External reference
Boundary singularities for weak solutions of semilinear elliptic problems
10.1016/j.jfa.2007.05.023 · 2007 · External reference
Definition of fractional Laplacian for functions with polynomial growth
10.4171/rmi/1079 · 2019 · External reference
A direct method of moving planes for fractional Laplacian equations in the unit ball
10.3934/cpaa.2016015 · 2016 · External reference
Fractional calculus for power functions and eigenvalues of the fractional Laplacian
10.2478/s13540-012-0038-8 · 2012 · External reference
Entire 𝑠-harmonic functions are affine
10.1090/proc/13021 · 2016 · External reference
Unresolved reference
2012 · External reference
The Dirichlet problem for nonlocal operators
10.1007/s00209-014-1394-3 · 2015 · External reference
Singularities and asymptotics for the equation Δ_{𝑔}𝑢-𝑢^{𝑞}=𝑆𝑢
10.1512/iumj.1993.42.42068 · 1993 · External reference
Global and local behavior of positive solutions of nonlinear elliptic equations
10.1002/cpa.3160340406 · 1981 · External reference
10.1007/978-3-642-61798-0
10.1007/978-3-642-61798-0 · 1983 · External reference
Recent progress on the fractional Laplacian in conformal geometry
10.1515/9783110571561-008 · 2018 · External reference
Singular solutions of fractional order conformal Laplacians
10.1007/s12220-011-9217-9 · 2012 · External reference
Fractional conformal Laplacians and fractional Yamabe problems
10.2140/apde.2013.6.1535 · 2013 · External reference
Further results on the fractional Yamabe problem: the umbilic case
10.1007/s12220-017-9794-3 · 2018 · External reference
Scattering matrix in conformal geometry
10.1007/s00222-002-0268-1 · 2003 · External reference
On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions
10.4171/jems/456 · 2014 · External reference
On local behavior of singular positive solutions to nonlocal elliptic equations
10.1007/s00526-016-1102-8 · 2017 · External reference
Existence theorems of the fractional Yamabe problem
10.2140/apde.2018.11.75 · 2018 · External reference
The Yamabe problem
10.1090/s0273-0979-1987-15514-5 · 1987 · External reference
Isolated singularities in semilinear problems
10.1016/0022-0396(80)90018-2 · 1980 · External reference
Unresolved reference
1970 · External reference
Asymptotics of the Poisson kernel and Green’s functions of the fractional conformal Laplacian
10.3934/dcds.2022085 · 2022 · External reference
Elliptic theory of differential edge operators. I
10.1080/03605309108820815 · 1991 · External reference
Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature
10.1016/0022-1236(87)90097-8 · 1987 · External reference
A construction of singular solutions for a semilinear elliptic equation using asymptotic analysis
1996 · External reference
Constant scalar curvature metrics with isolated singularities
10.1215/s0012-7094-99-09913-1 · 1999 · External reference
Conformally flat metrics of constant positive scalar curvature on subdomains of the sphere
1991 · External reference
Unresolved reference
External reference
The Yamabe problem on subdomains of even-dimensional spheres
10.12775/tmna.1995.036 · 1995 · External reference
Existence and convergence of positive weak solutions of -Δ𝑢=𝑢^{𝑛/(𝑛-2)} in bounded domains of 𝐑ⁿ,𝐧≥3
10.1007/bf01191296 · 1993 · External reference
10.1007/978-3-030-18222-9
10.1007/978-3-030-18222-9 · 2019 · External reference
The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
10.1016/j.matpur.2013.06.003 · 2014 · External reference
Conformally flat manifolds, Kleinian groups and scalar curvature
10.1007/bf01393992 · 1988 · External reference
The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation
10.1002/cpa.3160410305 · 1988 · External reference
Variational theory for the total scalar curvature functional for Riemannian metrics and related topics
10.1007/bfb0089180 · 1989 · External reference
Isolated singularities of solutions of quasi-linear equations
10.1007/bf02391778 · 1965 · External reference
Variational methods for non-local operators of elliptic type
10.3934/dcds.2013.33.2105 · 2013 · External reference
10.1093/oso/9780198505730.001.0001
10.1093/oso/9780198505730.001.0001 · 2000 · External reference
Comportement asymptotique des solutions d’équations elliptiques semi-linéaires dans 𝐑^{𝐍}
10.1007/bf01811717 · 1981 · External reference
Local behavior of solutions to a fractional equation with isolated singularity and critical Serrin exponent
10.3934/dcds.2022044 · 2022 · External reference
On isolated singularities of fractional semi-linear elliptic equations
10.1016/j.anihpc.2020.07.003 · 2021 · External reference
Exact asymptotic behavior of singular positive solutions of fractional semi-linear elliptic equations
10.1090/proc/14448 · 2019 · External reference
Classification of solutions for an integral equation
10.1002/cpa.20116 · ExternalCitation · doi-reference
Global and local behavior of positive solutions of nonlinear elliptic equations
10.1002/cpa.3160340406 · ExternalCitation · doi-reference
The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation
10.1002/cpa.3160410305 · ExternalCitation · doi-reference
Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth
10.1002/cpa.3160420304 · ExternalCitation · doi-reference
10.1007/978-3-030-18222-9
10.1007/978-3-030-18222-9 · ExternalCitation · doi-reference
10.1007/978-3-642-61798-0
10.1007/978-3-642-61798-0 · ExternalCitation · doi-reference
Existence and convergence of positive weak solutions of -Δ𝑢=𝑢^{𝑛/(𝑛-2)} in bounded domains of 𝐑ⁿ,𝐧≥3
10.1007/bf01191296 · ExternalCitation · doi-reference
Local behavior of solutions of some elliptic equations
10.1007/bf01210610 · ExternalCitation · doi-reference
Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations
10.1007/bf01243922 · ExternalCitation · doi-reference
Conformally flat manifolds, Kleinian groups and scalar curvature
10.1007/bf01393992 · ExternalCitation · doi-reference
Comportement asymptotique des solutions d’équations elliptiques semi-linéaires dans 𝐑^{𝐍}
10.1007/bf01811717 · ExternalCitation · doi-reference
Isolated singularities of solutions of quasi-linear equations
10.1007/bf02391778 · ExternalCitation · doi-reference
Existence of positive weak solutions with a prescribed singular set of semilinear elliptic equations
10.1007/bf02921937 · ExternalCitation · doi-reference
Variational theory for the total scalar curvature functional for Riemannian metrics and related topics
10.1007/bfb0089180 · ExternalCitation · doi-reference
Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities
10.1007/s00205-014-0722-4 · ExternalCitation · doi-reference
Delaunay-type singular solutions for the fractional Yamabe problem
10.1007/s00208-016-1483-1 · ExternalCitation · doi-reference
The Dirichlet problem for nonlocal operators
10.1007/s00209-014-1394-3 · ExternalCitation · doi-reference
Scattering matrix in conformal geometry
10.1007/s00222-002-0268-1 · ExternalCitation · doi-reference
Isolated boundary singularities of semilinear elliptic equations
10.1007/s00526-010-0337-z · ExternalCitation · doi-reference
On local behavior of singular positive solutions to nonlocal elliptic equations
10.1007/s00526-016-1102-8 · ExternalCitation · doi-reference
Existence of positive weak solutions for fractional Lane-Emden equations with prescribed singular sets
10.1007/s00526-018-1425-8 · ExternalCitation · doi-reference
The sharp exponent in the study of the nonlocal Hénon equation in ℝ^{ℕ}: a Liouville theorem and an existence result
10.1007/s00526-020-01763-z · ExternalCitation · doi-reference
Singular solutions of fractional order conformal Laplacians
10.1007/s12220-011-9217-9 · ExternalCitation · doi-reference
Further results on the fractional Yamabe problem: the umbilic case
10.1007/s12220-017-9794-3 · ExternalCitation · doi-reference
Isolated singularities in semilinear problems
10.1016/0022-0396(80)90018-2 · ExternalCitation · doi-reference
Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature
10.1016/0022-1236(87)90097-8 · ExternalCitation · doi-reference
Fractional Laplacian in conformal geometry
10.1016/j.aim.2010.07.016 · ExternalCitation · doi-reference
A direct method of moving planes for the fractional Laplacian
10.1016/j.aim.2016.11.038 · ExternalCitation · doi-reference
On isolated singularities of fractional semi-linear elliptic equations
10.1016/j.anihpc.2020.07.003 · ExternalCitation · doi-reference
Finite Morse index solutions of an elliptic equation with supercritical exponent
10.1016/j.jde.2011.02.005 · ExternalCitation · doi-reference
Boundary singularities for weak solutions of semilinear elliptic problems
10.1016/j.jfa.2007.05.023 · ExternalCitation · doi-reference
Uniqueness for the nonlocal Liouville equation in ℝ
10.1016/j.jfa.2022.109712 · ExternalCitation · doi-reference
The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
10.1016/j.matpur.2013.06.003 · ExternalCitation · doi-reference
Fast and slow decay solutions for supercritical fractional elliptic problems in exterior domains
10.1017/prm.2020.91 · ExternalCitation · doi-reference
An extension problem related to the fractional Laplacian
10.1080/03605300600987306 · ExternalCitation · doi-reference
An analytic construction of singular solutions related to a critical Yamabe problem
10.1080/03605302.2020.1784209 · ExternalCitation · doi-reference
Elliptic theory of differential edge operators. I
10.1080/03605309108820815 · ExternalCitation · doi-reference
Entire 𝑠-harmonic functions are affine
10.1090/proc/13021 · ExternalCitation · doi-reference
Exact asymptotic behavior of singular positive solutions of fractional semi-linear elliptic equations
10.1090/proc/14448 · ExternalCitation · doi-reference
The Yamabe problem
10.1090/s0273-0979-1987-15514-5 · ExternalCitation · doi-reference
10.1093/oso/9780198505730.001.0001
10.1093/oso/9780198505730.001.0001 · ExternalCitation · doi-reference
Classification of isolated singularities of nonnegative solutions to fractional semi-linear elliptic equations and the existence results
10.1112/jlms.12104 · ExternalCitation · doi-reference
On higher-dimensional singularities for the fractional Yamabe problem: a nonlocal Mazzeo-Pacard program
10.1215/00127094-2019-0034 · ExternalCitation · doi-reference
Constant scalar curvature metrics with isolated singularities
10.1215/s0012-7094-99-09913-1 · ExternalCitation · doi-reference
The Yamabe problem on subdomains of even-dimensional spheres
10.12775/tmna.1995.036 · ExternalCitation · doi-reference
On isolated singularities in some nonlinear partial differential equations
10.1512/iumj.1983.32.32051 · ExternalCitation · doi-reference
Singularities and asymptotics for the equation Δ_{𝑔}𝑢-𝑢^{𝑞}=𝑆𝑢
10.1512/iumj.1993.42.42068 · ExternalCitation · doi-reference
10.1515/9783110269291
10.1515/9783110269291 · ExternalCitation · doi-reference
Recent progress on the fractional Laplacian in conformal geometry
10.1515/9783110571561-008 · ExternalCitation · doi-reference
A gluing approach for the fractional Yamabe problem with isolated singularities
10.1515/crelle-2018-0032 · ExternalCitation · doi-reference
Fractional conformal Laplacians and fractional Yamabe problems
10.2140/apde.2013.6.1535 · ExternalCitation · doi-reference
Existence theorems of the fractional Yamabe problem
10.2140/apde.2018.11.75 · ExternalCitation · doi-reference
Fractional calculus for power functions and eigenvalues of the fractional Laplacian
10.2478/s13540-012-0038-8 · ExternalCitation · doi-reference
Some observations on the Green function for the ball in the fractional Laplace framework
10.3934/cpaa.2016.15.657 · ExternalCitation · doi-reference
A direct method of moving planes for fractional Laplacian equations in the unit ball
10.3934/cpaa.2016015 · ExternalCitation · doi-reference
Qualitative properties of solutions for an integral equation
10.3934/dcds.2005.12.347 · ExternalCitation · doi-reference
Variational methods for non-local operators of elliptic type
10.3934/dcds.2013.33.2105 · ExternalCitation · doi-reference
Large 𝑆-harmonic functions and boundary blow-up solutions for the fractional Laplacian
10.3934/dcds.2015.35.5555 · ExternalCitation · doi-reference
Local behavior of solutions to a fractional equation with isolated singularity and critical Serrin exponent
10.3934/dcds.2022044 · ExternalCitation · doi-reference
Asymptotics of the Poisson kernel and Green’s functions of the fractional conformal Laplacian
10.3934/dcds.2022085 · ExternalCitation · doi-reference
On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions
10.4171/jems/456 · ExternalCitation · doi-reference
Isolated singularities for a semilinear equation for the fractional Laplacian arising in conformal geometry
10.4171/rmi/1038 · ExternalCitation · doi-reference
Definition of fractional Laplacian for functions with polynomial growth
10.4171/rmi/1079 · ExternalCitation · doi-reference
ODE methods in non-local equations
10.4208/jms.v53n4.20.01 · ExternalCitation · doi-reference
