On a weighted trace embedding and applications to critical boundary problems†

DOI10.1002/mana.201900012zbMath1523.35016OpenAlexW3133680016MaRDI QIDQ6081898

Lucas C. F. Ferreira, Marcelo F. Furtado, João Pablo P. da Silva, Everaldo Souto de Medeiros

Publication date: 5 October 2023

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201900012

zbMATH Keywords

self-similar solutionsnonlinear boundary conditionsbest constanthalf-spaceweighted trace embedding

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Initial-boundary value problems for second-order parabolic equations (35K20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (3)

Elliptic equations with critical and supercritical growth at the boundary ⋮ Critical boundary value problems in the upper half-space ⋮ Elliptic problems in the half-space with nonlinear critical boundary conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Stability of steady states for the heat equation with nonlinear boundary conditions
• On the heat equation with nonlinearity and singular anisotropic potential on the boundary
• Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
• The concentration-compactness principle in the calculus of variations. The limit case. I
• Exterior problems in the half-space for the Laplace operator in weighted Sobolev spaces
• Existence of positive solutions of a semilinear elliptic equation in \(\mathbb{R}_+^n\) with a nonlinear boundary condition
• On a Neumann problem involving two critical Sobolev exponents: Remarks on geometrical and topological aspects
• On the nonlinear Neumann problem involving the critical Sobolev exponent on the boundary.
• Minimax theorems
• The Nehari manifold for a semilinear elliptic problem with the nonlinear boundary condition
• Dual variational methods in critical point theory and applications
• Positive solutions of elliptic problems involving both critical Sobolev nonlinearities on exterior regions
• Compact imbeddings of weighted Sobolev spaces on unbounded domains
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Bounds of global solutions of parabolic problems with nonlinear boundary conditions
• Nondegeneracy of blowup for semilinear heat equations
• Weighted Sobolev spaces and embedding theorems
• Asymptotically self‐similar blow‐up of semilinear heat equations
• Trace Theorems for Anisotropic Weighted SOBOLEV Spaces in a Corner
• Variational problems related to self-similar solutions of the heat equation
• Remark on Compactness of Imbeddings in Weighted Spaces
• Nonlinear boundary value problems in weighted sobolev spaces
• Existence and multiplicity of self-similar solutions for heat equations with nonlinear boundary conditions

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