Generalized Polya-szego Inequality
H.Hajaiej
TL;DR
This paper extends the Polya inequality to a broader class of functions involving both a function and its gradient, providing new insights into symmetrization inequalities and their equality cases.
Contribution
It generalizes the Polya inequality to integrands depending on a function and its gradient, including conditions for equality.
Findings
Established the Polya inequality for gradient-dependent integrands
Identified cases of equality in the symmetrization inequality
Extended the applicability of Polya inequality to new function classes
Abstract
In this paper we prove the Polya-Inequality for integrands depending on a function u and its gradient. We also establish cases of equality in this symmetrization inequality.
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Taxonomy
TopicsMathematical Inequalities and Applications · Nonlinear Partial Differential Equations · Analytic and geometric function theory