Bounds for Sobolev Embedding Constants in Non-simply Connected Planar Domains

DOI10.1007/978-3-030-73363-6_6zbMath1473.35012OpenAlexW3171185488MaRDI QIDQ5153538

Gazzola, Filippo, Gianmarco Sperone

Publication date: 30 September 2021

Published in: Geometric Properties for Parabolic and Elliptic PDE's (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-73363-6_6

zbMATH Keywords

symmetrizationbounded non-simply connected planar domainpyramidal functions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

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Cites Work

• The art of rearranging
• Some critical quasilinear elliptic problems with mixed Dirichlet-Neumann boundary conditions: relation with Sobolev and Hardy-Sobolev optimal constants
• Steiner symmetrization is continuous in \(W^{1,p}\)
• Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
• Steady Navier-Stokes equations in planar domains with obstacle and explicit bounds for unique solvability
• On optimization problems with prescribed rearrangements
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