Viscosity solutions and the minimal surface system
Ovidiu Savin
TL;DR
This paper introduces a definition of viscosity solutions for the minimal surface system and establishes a regularity theorem analogous to Allard's, advancing the understanding of minimal surfaces in a generalized framework.
Contribution
It provides the first formulation of viscosity solutions for the minimal surface system and proves a regularity result within this new setting.
Findings
Established a viscosity solution framework for minimal surface systems
Proved a version of Allard regularity theorem in this context
Enhanced the theoretical understanding of minimal surfaces
Abstract
We give a definition of viscosity solution for the minimal surface system and prove a version of Allard regularity theorem in this setting.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering