The Dirichlet energy integral on intervals in variable exponent Sobolev spaces

DOI10.4171/ZAA/1179zbMath1046.46027OpenAlexW1991626983MaRDI QIDQ1432985

Mika Koskenoja, Peter A. Hästö, Petteri Harjulehto

Publication date: 15 June 2004

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/zaa/1179

zbMATH Keywords

zero boundary valuesSobolev capacityvariable exponent Sobolev spaceminimizing problemDirichlet energy integral

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) Other generalizations (nonlinear potential theory, etc.) (31C45)

Related Items (10)

An obstacle problem and superharmonic functions with nonstandard growth ⋮ The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values ⋮ Some properties of thinness and fine topology with relative capacity ⋮ Unbounded supersolutions of nonlinear equations with nonstandard growth ⋮ Regularity of minima: an invitation to the dark side of the calculus of variations. ⋮ Minimizers of the variable exponent, non-uniformly convex Dirichlet energy ⋮ Overview of differential equations with non-standard growth ⋮ Regularity for minimizers of double phase functionals with mild transition and regular coefficients ⋮ Existence of multiple solutions for weighted \(p(r)\)-Laplacian equation Dirichlet problems ⋮ Harnack's inequality for \( p(\cdot\))-harmonic functions with unbounded exponent \(p\)

Cites Work

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