Definitions of Sobolev classes on metric spaces

From MaRDI portal
Publication:1807908

DOI10.5802/aif.1742zbMath0938.46037OpenAlexW2168152212WikidataQ109947381 ScholiaQ109947381MaRDI QIDQ1807908

Bruno Franchi, Piotr Hajłasz, Pekka Koskela

Publication date: 24 November 1999

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1999__49_6_1903_0



Related Items

A simple proof of reflexivity and separability of N^{1,p} Sobolev spaces, Several equivalent characterizations of fractional Hajłasz-Morrey-Sobolev spaces, Higher integrability for vector-valued parabolic quasi-minimizers on metric measure spaces, Nonsmooth calculus, Pointwise characterizations of Besov and Triebel-Lizorkin spaces with generalized smoothness and their applications, The Stepanov differentiability theorem in metric measure spaces, Axiomatic theory of Sobolev spaces, Sobolev embedding theorems and generalizations for functions on a metric measure space, Unnamed Item, Characterizations of sets of finite perimeter using heat kernels in metric spaces, Sobolev spaces on an arbitrary metric measure space: compactness of embeddings, The Cartan, Choquet and Kellogg properties for the fine topology on metric spaces, On extensions of Sobolev functions defined on regular subsets of metric measure spaces, Hölder regularity for parabolic De Giorgi classes in metric measure spaces, Vertical versus horizontal Sobolev spaces, Regularity of solutions to the fractional Cheeger-Laplacian on domains in metric spaces of bounded geometry, \(\Gamma\)-convergence of nonconvex integrals in Cheeger-Sobolev spaces and homogenization, Weighted norm inequalities, off-diagonal estimates and elliptic operators. I: General operator theory and weights, Newtonian Lorentz metric spaces, Characterizations of Sobolev spaces via averages on balls, Sobolev embedding theorems and their generalizations for maps defined on topological spaces with measures, A Rademacher type theorem for Hamiltonians \(H(x, p)\) and an application to absolute minimizers, Neumann \(p\)-Laplacian problems with a reaction term on metric spaces, Differentiability of \(p\)-harmonic functions on metric measure spaces, Embedding theorems and a variational problem for functions on a metric measure space, Existence and almost uniqueness for \(p\)-harmonic Green functions on bounded domains in metric spaces, An invariant Harnack inequality for a class of subelliptic operators under global doubling and Poincaré assumptions, and applications, Analytic approaches and harmonic functions on Alexandrov spaces with nonnegative Ricci curvature, Unnamed Item, Relaxation of nonconvex unbounded integrals with general growth conditions in Cheeger-Sobolev spaces, Characterizations of Orlicz-Sobolev spaces by means of generalized Orlicz-Poincaré inequalities, Existence of parabolic minimizers to the total variation flow on metric measure spaces, Removable sets for Newtonian Sobolev spaces and a characterization of \(p\)-path almost open sets, Sobolev spaces on compact groups, The Cheeger problem in abstract measure spaces, Almost-Riemannian manifolds do not satisfy the curvature-dimension condition, The Perron method for \(p\)-harmonic functions in metric spaces., Gradient estimate for solutions to Poisson equations in metric measure spaces, New characterizations of Sobolev spaces on the Heisenberg group, Parabolic flow on metric measure spaces, Is an Orlicz-Poincaré inequality an open ended condition, and what does that mean?, Polar sets on metric spaces, New Sobolev spaces via generalized Poincaré inequalities on metric measure spaces, Mappings of finite inner distortion: global homeomorphism theorem, Characterization of Orlicz--Sobolev space, A note on the extension of BV functions in metric measure spaces, Sobolev-Lorentz spaces in the Euclidean setting and counterexamples, A REPRESENTATION FORMULA FOR THE p-ENERGY OF METRIC SPACE-VALUED SOBOLEV MAPS, Weak Fubini property and infinity harmonic functions in Riemannian and sub-Riemannian manifolds, Abstract and concrete tangent modules on Lipschitz differentiability spaces, Weighted Sobolev spaces on metric measure spaces, Local behavior of \(p\)-harmonic Green's functions in metric spaces, SOBOLEV CLASSES AND HORIZONTAL ENERGY MINIMIZERS BETWEEN CARNOT–CARATHÉODORY SPACES, New Sobolev spaces via generalized Poincaré inequalities on metric measure spaces, The grand Lusin‐area characterization of Hajłasz‐Sobolev spaces and Triebel‐Lizorkin spaces, Carleson type estimates for \(p\)-harmonic functions and the conformal Martin boundary of John domains in metric measure spaces, Characterizations of Sobolev spaces in Euclidean spaces and Heisenberg groups, An atomic decomposition of the Hajłasz Sobolev space on manifolds, On Cheeger and Sobolev differentials in metric measure spaces, Morrey-Sobolev spaces on metric measure spaces, Existence of parabolic minimizers on metric measure spaces, Sobolev Mappings between Manifolds and Metric Spaces, Discrete convolutions of \(\text{BV}\) functions in quasiopen sets in metric spaces, Density of Lipschitz mappings in the class of Sobolev mappings between metric spaces, Existence of variational solutions to a Cauchy-Dirichlet problem with time-dependent boundary data on metric measure spaces, A theory of Besov and Triebel-Lizorkin spaces on metric measure spaces modeled on Carnot-Carathéodory spaces, Relaxation and integral representation for functionals of linear growth on metric measure spaces, Lower semicontinuity of integrals of the calculus of variations in Cheeger-Sobolev spaces, Boundary measures, generalized Gauss-Green formulas, and mean value property in metric measure spaces, Sobolev functions in the critical case are uniformly continuous in $s$-Ahlfors regular metric spaces when $s\le 1$, Integral representation and relaxation of local functionals on Cheeger-Sobolev spaces, Maximal Functions Measuring Smoothness, On the essential self-adjointness of singular sub-Laplacians, Fractional Hajłasz–Morrey–Sobolev spaces on quasi-metric measure spaces, On the locally branched Euclidean metric gauge, \(L^1\rightarrow L^q\) Poincaré inequalities for \(0<q<1\) imply representation formulas, Characterizations of second order Sobolev spaces, Fat sets and pointwise boundary estimates for \(p\)-harmonic functions in metric spaces, Newton-Besov spaces and Newton-Triebel-Lizorkin spaces on metric measure spaces, Sobolev inequalities in arbitrary domains



Cites Work