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Sobolev Spaces and Calculus of Variations on Fractals

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Publication:5137262

DOI10.1142/9789811215537_0013zbMATH Open1466.46032arXiv1805.04456OpenAlexW3175836910MaRDI QIDQ5137262

Author name not available (Why is that?)

Publication date: 2 December 2020

Published in: (Search for Journal in Brave)

Abstract: The present note contains a review of p-energies and Sobolev spaces on metric measure spaces that carry a strongly local regular Dirichlet form. These Sobolev spaces are then used to generalize some basic results from the calculus of variations, such as the existence of minimizers for convex functionals and certain constrained mimimization problems. This applies to a number of non-classical situations such as degenerate diffusions, superpositions of diffusions and diffusions on fractals or on products of fractals.


Full work available at URL: https://arxiv.org/abs/1805.04456



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