Axiomatic theory of Sobolev spaces
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Publication:1348585
DOI10.1016/S0723-0869(01)80018-9zbMath1006.46023OpenAlexW2159927953MaRDI QIDQ1348585
Vladimir Gol'dshtein, Marc Troyanov
Publication date: 27 February 2003
Published in: Expositiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0723-0869(01)80018-9
Related Items
The Stepanov differentiability theorem in metric measure spaces, A new approach to Sobolev spaces in metric measure spaces, Sobolev embedding theorems and generalizations for functions on a metric measure space, Partial derivatives in the nonsmooth setting, Sobolev spaces on an arbitrary metric measure space: compactness of embeddings, The Hajłasz capacity density condition is self-improving, \(\Gamma\)-convergence of nonconvex integrals in Cheeger-Sobolev spaces and homogenization, Wiener criterion on metric spaces: boundary regularity in axiomatic and Poincaré-Sobolev spaces, Sobolev embedding theorems and their generalizations for maps defined on topological spaces with measures, Embedding theorems and a variational problem for functions on a metric measure space, Relaxation of nonconvex unbounded integrals with general growth conditions in Cheeger-Sobolev spaces, Metric space mappings connected with Sobolev-type function classes, Differential structure associated to axiomatic Sobolev spaces, The connectivity at infinity of a manifold and \(L^{q, p}\)-Sobolev inequalities, Riemannian polyhedra and Liouville-type theorems for harmonic maps, A note on the extension of BV functions in metric measure spaces, \(q\)-parabolicity of stratified pseudomanifolds and other singular spaces, Maximal function estimates and self-improvement results for Poincaré inequalities, A Meyers type regularity result for approximations of second order elliptic operators by P1 finite elements, Interpolation of Sobolev spaces, Littlewood-Paley inequalities and Riesz transforms on graphs, An axiomatic approach to gradients with applications to Dirichlet and obstacle problems beyond function spaces, A Universality Property of Sobolev Spaces in Metric Measure Spaces, On subadditive theorems for group actions and homogenization, Axiomatic regularity on metric spaces, Lower semicontinuity of integrals of the calculus of variations in Cheeger-Sobolev spaces, Characterisation of upper gradients on the weighted Euclidean space and applications, Real interpolation of Sobolev spaces associated to a weight, Integral representation and relaxation of local functionals on Cheeger-Sobolev spaces, The \(p\)-Royden and \(p\)-harmonic boundaries for metric measure spaces, Capacities in metric spaces, Tensorization of Cheeger energies, the space \(H^{1, 1}\) and the area formula for graphs
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