A Poincaré inequality in a Sobolev space with a variable exponent

DOI10.1007/s11401-011-0648-1zbMath1305.46026OpenAlexW2009034023MaRDI QIDQ741421

Philippe G. Ciarlet, Gheorghe Dinca

Publication date: 12 September 2014

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-011-0648-1

zbMATH Keywords

Poincaré inequalitySobolev spaces with variable exponent

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities for sums, series and integrals (26D15) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (7)

Existence of weak solutions for a nonlinear problem involving \(p(\cdot)\)-Laplacian operator with mixed boundary conditions ⋮ A unified divergent approach to Hardy-Poincaré inequalities in classical and variable Sobolev spaces ⋮ Kirchhoff-Type Problem with Mixed Boundary Condition in a Variable Exponent Sobolev Space ⋮ Global regularity of weak solutions for steady motions of electrorheological fluids in 3D smooth domain ⋮ Removability of zero modular capacity sets ⋮ Poincaré-type inequalities in Musielak spaces ⋮ FRÉCHET DIFFERENTIABILITY OF THE NORM IN A SOBOLEV SPACE WITH A VARIABLE EXPONENT

Cites Work

• Poincaré inequalities in reflexive cones
• Boundary trace embedding theorems for variable exponent Sobolev spaces
• A priori estimates for the vector \(p\)-Laplacian with potential boundary conditions
• AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
• Maximal function on generalized Lebesgue spaces L^p(⋅)
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
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