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
latticeBanach spacesDirichlet problemmetric spaceRayleigh quotientvariational problemsfirst eigenvaluepartial orderobstacle problemgeneralized Sobolev spacegradient relationnoncommutative function spacesoperator-valued functionPoincaré setRellich-Kondrachov conetrace class ideal
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)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Wiener criterion on metric spaces: boundary regularity in axiomatic and Poincaré-Sobolev spaces
- Nonlinear potential theory on metric spaces
- Quasiconformal maps in metric spaces with controlled geometry
- Differentiability of Lipschitz functions on metric measure spaces
- Axiomatic theory of Sobolev spaces
- Sobolev classes of Banach space-valued functions and quasiconformal mappings
- Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
- Theory of operator algebras. II
- Capacities in metric spaces
- Sobolev spaces on an arbitrary metric space
- Obstacle and Dirichlet problems on arbitrary nonopen sets in metric spaces, and fine topology
- The Poincaré inequality is an open ended condition
- Harnack's inequality for a nonlinear eigenvalue problem on metric spaces
- Axiomatic regularity on metric spaces
- \(c_ p\)
- Change of variables for absolutely continuous functions
- Minimal weak upper gradients in Newtonian spaces based on quasi-Banach function lattices
- Clarkson and Random Clarkson Inequalities forLr(X)
- Sobolev met Poincaré
- Sobolev Spaces on Metric Measure Spaces
- Order in Operator Algebras
- Formes linéaires sur un anneau d'opérateurs
- Theory of operator algebras I.
- Harmonic functions on metric spaces
This page was built for publication: An axiomatic approach to gradients with applications to Dirichlet and obstacle problems beyond function spaces
