Gradient estimate of the solutions to Hessian equations with oblique boundary value
Peihe Wang
TL;DR
This paper derives a global gradient estimate for solutions to Hessian equations with oblique boundary conditions, advancing understanding of boundary value problems in nonlinear PDEs.
Contribution
It provides the first a priori gradient estimate for admissible solutions to Hessian equations with oblique boundary conditions.
Findings
Established a global gradient estimate for admissible solutions.
Extended the theory of Hessian equations to include oblique boundary conditions.
Enhanced the mathematical understanding of boundary value problems in nonlinear PDEs.
Abstract
In this paper, we study Hessian equations with prescribed contact angle boundary value or oblique derivative boundary value and finally derive the a priori global gradient estimate for the admissible solutions.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Nonlinear Partial Differential Equations