GEOMETRY OF SOBOLEV SPACES WITH VARIABLE EXPONENT AND A GENERALIZATION OF THE p-LAPLACIAN

DOI10.1142/S0219530509001451zbMath1189.46010MaRDI QIDQ3646144

Pavel Matei, Gheorghe Dinca

Publication date: 19 November 2009

Published in: Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

duality mapping\(p\)-Laplacian operatoruniformly convex spaceLebesgue space with variable exponentsmooth spaceSobolev space with variable exponent

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Degenerate elliptic equations (35J70) Geometry and structure of normed linear spaces (46B20) Duality and reflexivity in normed linear and Banach spaces (46B10)

Related Items (6)

Modular-Proximal Gradient Algorithms in Variable Exponent Lebesgue Spaces ⋮ Stability of the norm-eigenfunctions of the \(p(\cdot)\)-Laplacian ⋮ Dual descent regularization algorithms in variable exponent Lebesgue spaces for imaging ⋮ Geometry of Sobolev spaces with variable exponent: Smoothness and uniform convexity ⋮ \(\Gamma\)-convergence of the energy functionals for the variable exponent \(p(\cdot)\)-Laplacian and stability of the minimizers with respect to integrability ⋮ FRÉCHET DIFFERENTIABILITY OF THE NORM IN A SOBOLEV SPACE WITH A VARIABLE EXPONENT

Cites Work

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• Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spacesLp(·) andWk,p(·)
• Une méthode de point fixe pour le p-laplacien
• On a progress in the theory of lebesgue spaces with variable exponent: maximal and singular operators
• Eine Verallgemeinerung der Sobolewschen Räume und ihre Anwendung zur Lösung von Variationsproblemen
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

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