On a differential inclusion related to the Born-Infeld equations
Stefan M\"uller, Mariapia Palombaro
TL;DR
This paper investigates a differential inclusion connected to the Born-Infeld equations, extending Maxwell's equations, by applying Gromov's convex integration method to divergence-free fields.
Contribution
It introduces a novel application of convex integration to analyze a differential relation related to Born-Infeld equations.
Findings
Establishment of a differential inclusion framework for Born-Infeld equations
Application of convex integration to divergence-free fields in this context
Insights into the structure of solutions to the differential relation
Abstract
We study a partial differential relation that arises in the context of the Born-Infeld equations (an extension of the Maxwell's equations) by using Gromov's method of convex integration in the setting of divergence free fields.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Spectral Theory in Mathematical Physics