The best constant for the Sobolev trace embedding from \(W^{1,1}(\Omega)\) into \(L^1(\partial\Omega)\)

DOI10.1016/j.na.2004.07.051zbMath1108.35067OpenAlexW2098293590MaRDI QIDQ1765208

Julio D. Rossi, José M. Mazón Ruiz, Fuensanta Andreu

Publication date: 23 February 2005

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2004.07.051

zbMATH Keywords

functions of bounded variationSobolev trace embedding

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Critical exponents in context of PDEs (35B33) Linear function spaces and their duals (46E99)

Related Items (10)

A Neumann problem for the \(p(x)\)-Laplacian with \(p=1\) in a subdomain ⋮ On the best constants in Sobolev inequalities on the solid torus in the limit case \(p = 1\) ⋮ Mathematical modeling, analysis and numerical approximation of second-order elliptic problems with inclusions ⋮ Poincaré trace inequalities in \(BV({\mathbb {B}}^n)\) with non-standard normalization ⋮ Estimates of the best Sobolev constant of the embedding of \(\mathrm{BV}(\Omega)\) into \(L^1(\partial \Omega)\) and related shape optimization problems ⋮ Balls minimize trace constants in BV ⋮ Asymmetric Poincaré inequalities and solvability of capillarity problems ⋮ Minimizing \(L^{\infty }\)-norm functional on divergence-free fields ⋮ Vector analysis on symmetric manifolds and Sobolev inequalities ⋮ On a conjectured reverse Faber-Krahn inequality for a Steklov-type Laplacian eigenvalue

Cites Work

• Pairings between measures and bounded functions and compensated compactness
• On some nonlinear equation involving the 1-Laplacian and trace map inequalities
• The Cauchy problem for linear growth functionals
• Isolation and simplicity for the first eigenvalue of the \(p\)-Laplacian with a nonlinear boundary condition
• Minimizing total variation flow
• Weakly Differentiable Functions
• Existence results for the \(p\)-Laplacian with nonlinear boundary conditions
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