On a vector-valued generalisation of viscosity solutions for general PDE systems

Katzourakis, N. (2022) On a vector-valued generalisation of viscosity solutions for general PDE systems. Zeitschrift für Analysis und ihre Anwendungen, 41 (1/2). pp. 93-132. ISSN 1661-4534 doi: 10.4171/ZAA/1699

Abstract/Summary

We propose a theory of non-differentiable solutions which applies to fully nonlinear PDE systems and extends the theory of viscosity solutions of Crandall-Ishii-Lions to the vectorial case. Our key ingredient is the discovery of a notion of extremum for maps which extends min-max and allows “nonlinear passage of derivatives” to test maps. This new PDE approach supports certain stability and convergence results, preserving some basic features of the scalar viscosity counterpart. In this introductory work we focus on studying the analytical foundations of this new theory.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/105045
Identification Number/DOI	10.4171/ZAA/1699
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	EMS press
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