A new approach to Sobolev spaces in metric measure spaces

DOI10.1016/j.na.2016.04.010zbMath1371.46029arXiv1504.07778OpenAlexW782783950MaRDI QIDQ298321

Tomas Sjödin

Publication date: 20 June 2016

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.07778

zbMATH Keywords

Sobolev spacemass transportmetric measure space

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Potential theory on fractals and metric spaces (31E05) Analysis on metric spaces (30L99)

Cites Work

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• Nonlinear potential theory on metric spaces
• On extensions of Sobolev functions defined on regular subsets of metric measure spaces
• Quasiconformal maps in metric spaces with controlled geometry
• Differentiability of Lipschitz functions on metric measure spaces
• Axiomatic theory of Sobolev spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Sobolev spaces on an arbitrary metric space
• Gradient flows with metric and differentiable structures, and applications to the Wasserstein space
• Axiomatic regularity on metric spaces
• Nonsmooth calculus
• Sobolev Spaces on Metric Measure Spaces

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