Isocapacity Estimates for Hessian Operators
Jie Xiao, Ning Zhang
TL;DR
This paper introduces new potential-theoretic methods to identify isocapacity forms related to key inequalities for fully nonlinear Hessian operators, enhancing understanding of their geometric properties.
Contribution
It provides the first potential-theoretic analysis linking isocapacity forms with Sobolev and Moser-Trudinger inequalities for Hessian operators.
Findings
Derived geometrically equivalent isocapacity forms
Extended inequalities to fully nonlinear Hessian operators
Established new potential-theoretic framework
Abstract
Through a new powerful potential-theoretic analysis, this paper is devoted to discovering the geometrically equivalent isocapacity forms of Chou-Wang's Sobolev type inequality and Tian-Wang's Moser-Trudinger type inequality for the fully nonlinear Hessian operators.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Spectral Theory in Mathematical Physics · Advanced Mathematical Modeling in Engineering