On density of smooth functions in weighted Sobolev spaces with variable exponents

DOI10.1090/SPMJ/1396zbMath1354.46039OpenAlexW4253570894MaRDI QIDQ2797730

Vasilii V. Jikov, Mikhail D. Surnachev

Publication date: 6 April 2016

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/spmj/1396

zbMATH Keywords

variable exponentdensity of smooth functionsSobolev-Orlicz spacesLavrentiev phenomenonMuckenhoupt classes

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (8)

Existence and multiplicity of weak solutions for eigenvalue Robin problem with weighted \(p(.)\)-Laplacian ⋮ Existence and uniqueness of a weak solution of an integro-differential aggregation equation on a Riemannian manifold ⋮ Sobolev and Besov classes on infinite-dimensional spaces ⋮ Singular weighted Sobolev spaces and diffusion processes: an example (due to V.V. Zhikov) ⋮ New examples on Lavrentiev gap using fractals ⋮ Lavrentiev gap for some classes of generalized Orlicz functions ⋮ Hessian estimates for fully nonlinear equations via the large-\(M\)-inequality principle ⋮ On the KPZ equation with fractional diffusion: global regularity and existence results

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On variational problems and nonlinear elliptic equations with nonstandard growth conditions
• Density of smooth functions in weighted Sobolev spaces
• Variable Lebesgue spaces. Foundations and harmonic analysis
• Density of smooth functions in weighted Sobolev spaces with variable exponent
• Lebesgue and Sobolev spaces with variable exponents
• On the Hölder property of one elliptic equation
• On Lavrentiev's phenomenon
• On some variational problems
• An example of a space of \(L^{p(x)}\) on which the Hardy-Littlewood maximal operator is not bounded
• On Lavrent'ev's effect
• Density \(C_0^{\infty}(\mathbb{R}^n)\) in the generalized Sobolev spaces \(W^{m,p(x)}(\mathbb{R}^n)\).
• Sobolev capacity of the space \(W^{1,p(\cdot)} (\mathbb{R}^n)\)
• On the density of smooth functions in Sobolev-Orlicz spaces
• Maximal functions on Musielak--Orlicz spaces and generalized Lebesgue spaces
• The maximal operator on weighted variable Lebesgue spaces
• Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spacesLp(·) andWk,p(·)
• AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
• Weighted Sobolev spaces
• Regularity of nonstandard lagrangians ƒ(x, ξ)
• H = W
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

This page was built for publication: On density of smooth functions in weighted Sobolev spaces with variable exponents