An existence result for singular Finsler double phase problems

DOI10.1016/j.jde.2021.03.036zbMath1465.35148arXiv2011.03774OpenAlexW3136871169MaRDI QIDQ2020123

Patrick Winkert, Csaba Farkas

Publication date: 23 April 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.03774

zbMATH Keywords

critical exponentexistence resultsanisotropic double phase operator

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Second-order elliptic equations (35J15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quasilinear elliptic equations (35J62)

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Cites Work

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• Eigenvalues for double phase variational integrals
• An imbedding theorem for Musielak-Sobolev spaces
• Bounded minimisers of double phase variational integrals
• A characterization of the Wulff shape by an overdetermined anisotropic PDE
• Overdetermined anisotropic elliptic problems
• Singular Poisson equations on Finsler-Hadamard manifolds
• Uniform convexity and smoothness, and their applications in Finsler geometry
• Anisotropic motion by mean curvature in the context of Finsler geometry
• Isoperimetric inequalities, Wulff shape and related questions for strongly nonlinear elliptic operators
• Partial regularity for general systems of double phase type with continuous coefficients
• Singular \(p\)-Laplacian equations with superlinear perturbation
• Existence and multiplicity results for double phase problem
• Regularity for general functionals with double phase
• Existence results for double phase implicit obstacle problems involving multivalued operators
• Existence of solutions for double phase obstacle problems with multivalued convection term
• Singular Dirichlet \((p, q)\)-equations
• Double phase problems with variable growth and convection for the Baouendi-Grushin operator
• Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold
• Constant sign and nodal solutions for superlinear double phase problems
• Existence of solution for double-phase problem with singular weights
• Regularity for double phase variational problems
• Borderline gradient continuity of minima
• On the second Dirichlet eigenvalue of some nonlinear anisotropic elliptic operators
• Existence and uniqueness results for double phase problems with convection term
• Ground state and nodal solutions for a class of double phase problems
• Constant sign solutions for double phase problems with superlinear nonlinearity
• Regularity for double phase problems under additional integrability assumptions
• Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle
• Regularity for minimizers for functionals of double phase with variable exponents
• A quasilinear elliptic problem involving critical Sobolev exponents
• Harnack inequalities for double phase functionals
• Sharp estimates and existence for anisotropic elliptic problems with general growth in the gradient
• Regularity and existence of solutions of elliptic equations with p,q- growth conditions
• Existence and uniqueness of elliptic systems with double phase operators and convection terms
• Non-autonomous functionals, borderline cases and related function classes
• Applied Nonlinear Functional Analysis
• On the Equation div( | ∇u | p-2 ∇u) + λ | u | p-2 u = 0
• Remarks on a Finsler-Laplacian
• Existence results for double-phase problems via Morse theory
• Crystalline variational methods
• Combined effects of singular and superlinear nonlinearities in some singular boundary value problems.