ON THE DEFINITIONS OF SOBOLEV AND BV SPACES INTO SINGULAR SPACES AND THE TRACE PROBLEM

DOI10.1142/S0219199707002502zbMath1221.46031MaRDI QIDQ3502770

David Chiron

Publication date: 20 May 2008

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

zbMATH Keywords

Sobolev spacesmetric spacescompact embeddingtopological defectsBV maps

Mathematics Subject Classification ID

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

Related Items (18)

Two remarks on liftings of maps with values into \(S^1\). ⋮ Intrinsic structure of minimal discs in metric spaces ⋮ Crack Nucleation in Shells with Through-the-Thickness Microstructure ⋮ Topologies and measures on the space of functions of bounded variation taking values in a Banach or metric space ⋮ Harmonic mappings valued in the Wasserstein space ⋮ An intrinsic approach to manifold constrained variational problems ⋮ Convex functions defined on metric spaces are pulled back to subharmonic ones by harmonic maps ⋮ A Bourgain–Brezis–Mironescu characterization of higher order Besov–Nikol^{\prime }skii spaces ⋮ Integral energy characterization of Hajłasz-Sobolev spaces ⋮ Geometric Finite Elements ⋮ Estimates for the topological degree and related topics ⋮ Topological singular set of vector-valued maps. I: Applications to manifold-constrained Sobolev and BV spaces ⋮ \(\Gamma \)-convergence and Sobolev norms ⋮ Regularity of harmonic discs in spaces with quadratic isoperimetric inequality ⋮ A REPRESENTATION FORMULA FOR THE p-ENERGY OF METRIC SPACE-VALUED SOBOLEV MAPS ⋮ \(\Gamma\)-convergence, Sobolev norms, and BV functions ⋮ Lifting for manifold-valued maps of bounded variation ⋮ Multi-value microstructural descriptors for complex materials: analysis of ground states

Cites Work

• A new approach to Sobolev spaces and connections to \(\Gamma\)-convergence
• Differentiability of Lipschitz functions on metric measure spaces
• Equilibrium maps between metric spaces
• Global existence theorems for harmonic maps to nonlocally compact spaces
• On an open question about functions of bounded variation.
• Cheeger type Sobolev spaces for metric space targets
• Sobolev classes of Banach space-valued functions and quasiconformal mappings
• Harmonic maps into singular spaces and \(p\)-adic superrigidity for lattices in groups of rank one
• Sobolev spaces and harmonic maps for metric space targets
• Sobolev-type classes of functions with values in a metric space
• Some new characterizations of Sobolev spaces
• A new characterization of Sobolev spaces

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