ON GEOMETRIC PROPERTIES OF FUNCTIONS WITH GENERALIZED FIRST DERIVATIVES

DOI10.1070/RM1979v034n01ABEH002871zbMath0429.30017OpenAlexW2023144141MaRDI QIDQ3866363

Yu. G. Reshetnyak, Sergei Vodop'yanov, Vladimir Gol'dshtein

Publication date: 1979

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rm1979v034n01abeh002871

zbMATH Keywords

isoperimetric inequalityBibliographylattice isomorphismquasi-isometric mappingscapacity metricfunctions with generalized first derivativesorder- preserving operatorsremovable singularities for L1,p-spaces

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) Capacity and harmonic measure in the complex plane (30C85) Quasiconformal mappings in the complex plane (30C62) Representations of entire functions of one complex variable by series and integrals (30D10) Potentials and capacities, extremal length and related notions in higher dimensions (31B15) Cluster sets, prime ends, boundary behavior (30D40)

Related Items

On the isomorphism of Sobolev-type classes on metric spaces ⋮ On the equivalence of domains in the theory of Sobolev spaces with variable exponents ⋮ Estimates for variation of the first Dirichlet eigenvalue of the Laplace operator ⋮ The spectral estimates for the Neumann-Laplace operator in space domains ⋮ Injectivity and self-contact in nonlinear elasticity ⋮ Unnamed Item ⋮ Berger's isoperimetric problem and minimal immersions of surfaces ⋮ The boundary behavior of $\mathcal Q_{p,q}$-homeomorphisms ⋮ Estimates for Dirichlet eigenvalues of divergence form elliptic operators in non-Lipschitz domains ⋮ On the boundary behavior of weak \((p, q)\)-quasiconformal mappings ⋮ On closability of classical Dirichlet forms. ⋮ A quasi-variational problem in nonlinear elasticity ⋮ Composition operators on Hardy-Sobolev spaces and BMO-quasiconformal mappings ⋮ On Lipschitz approximations in second order Sobolev spaces and the change of variables formula ⋮ Composition operators on Sobolev spaces and Neumann eigenvalues ⋮ Whitney's problem on extendability of functions and an intrinsic metric ⋮ Boundary behavior and equicontinuity for families of mappings in terms of prime ends ⋮ Example of a smooth homeomorphism violating the Luzin \(N^{-1}\) property ⋮ Prime ends and Orlicz–Sobolev classes ⋮ Global invertibility of Sobolev functions and the interpenetration of matter ⋮ Extension of smooth functions from finitely connected planar domains ⋮ Infinite Energy Cavitating Solutions: A Variational Approach