Wolff type potential estimates and application to nonlinear equations with negative exponents

DOI10.3934/DCDS.2015.35.2067zbMath1307.45005OpenAlexW2329804042MaRDI QIDQ484422

Yutian Lei

Publication date: 7 January 2015

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2015.35.2067

zbMATH Keywords

asymptotic behaviorpositive solutionconformal geometryradial solutionWolff potential\(k\)-Hessian equation\(\gamma\)-Laplace equationWolff-type integral equation

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Asymptotics of solutions to integral equations (45M05) Systems of nonlinear integral equations (45G15) Positive solutions of integral equations (45M20) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (3)

Wolff-type integral system including m equations ⋮ On the Wolff-type integral system with negative exponents ⋮ A direct method of moving planes for the fractional \(p\)-Laplacian system with negative powers

Cites Work

• Unnamed Item
• The properties of positive solutions to an integral system involving Wolff potential
• Asymptotic radial symmetry and growth estimates of positive solutions to weighted Hardy-Littlewood-Sobolev system of integral equations
• On the integral systems with negative exponents
• Exact solutions of nonlinear conformally invariant integral equations in \(\mathbf R^3\)
• Gradient potential estimates
• Regularity of solutions for an integral system of Wolff type
• Decay rates for solutions of an integral system of Wolff type
• Superharmonic functions are locally renormalized solutions
• Integrability and asymptotics of positive solutions of a \(\gamma \)-Laplace system
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• Uniqueness theorem for integral equations and its application
• Classification of solutions of some nonlinear elliptic equations
• Structure theorems for positive radial solutions to \(\text{div}(| Du|^{m-2} Du)+K(| x|)u^ q=0\) in \(\mathbb{R}^ n\)
• The Wiener test and potential estimates for quasilinear elliptic equations
• Wolff potential estimates of superminimizers of Orlicz type Dirichlet integrals
• Wolff's inequality for radially nonincreasing kernels and applications to trace inequalities
• Remark on some conformally invariant integral equations: the method of moving spheres
• Thin sets in nonlinear potential theory
• Potential estimates for a class of fully nonlinear elliptic equations.
• Fast decay estimates for integrable solutions of the Lane-Emden type integral systems involving the Wolff potentials
• Liouville type theorems for integral equations and integral systems
• Radial symmetry of solutions for some integral systems of Wolff type
• Nonlinear biharmonic equations with negative exponents
• Quasilinear and Hessian equations of Lane-Emden type
• Liouville type results and regularity of the extremal solutions of biharmonic equation with negative exponents
• Wolff potential estimates for elliptic equations with nonstandard growth and applications
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Classification of solutions for an integral equation

This page was built for publication: Wolff type potential estimates and application to nonlinear equations with negative exponents