An axiomatic approach to gradients with applications to Dirichlet and obstacle problems beyond function spaces

DOI10.1016/j.na.2015.12.010zbMath1344.49006arXiv1501.06696OpenAlexW2048210MaRDI QIDQ5962924

Jana Björn, Anders Björn, Joakim Arnlind

Publication date: 25 February 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/1501.06696

zbMATH Keywords

latticeBanach spacesDirichlet problemmetric spaceRayleigh quotientvariational problemsfirst eigenvaluepartial orderobstacle problemgeneralized Sobolev spacegradient relationnoncommutative function spacesoperator-valued functionPoincaré setRellich-Kondrachov conetrace class ideal

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Spaces of vector- and operator-valued functions (46E40) Variational problems in a geometric measure-theoretic setting (49Q20) Variational methods for elliptic systems (35J50) Noncommutative measure and integration (46L51) Existence theories for problems in abstract spaces (49J27) Noncommutative function spaces (46L52) Variational methods for eigenvalues of operators (49R05) Potential theory on fractals and metric spaces (31E05) Nonlinear boundary value problems for nonlinear elliptic equations (35J66)

Related Items (1)

Sobolev functions on varifolds

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