Symmetry of intrinsically singular solutions of double phase problems
Stefano Biagi, Francesco Esposito, Eugenio Vecchi
TL;DR
This paper investigates the symmetry properties of positive singular solutions to double phase PDEs, focusing on the case where p<q<2, and introduces a relaxed capacity condition for the singular set.
Contribution
It extends previous work by analyzing symmetry under weaker capacity assumptions using an intrinsic capacity concept for the singular set.
Findings
Symmetry results are established for solutions with relaxed capacity conditions.
The analysis applies specifically to the case p<q<2.
The approach broadens the class of singular solutions understood in double phase problems.
Abstract
We continue the study of positive singular solutions of PDEs arising from double phase functionals started in [6]. In particular, we consider the case , and we relax the assumption on the capacity of the singular set using an intrinsic notion of capacity.
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Taxonomy
TopicsNonlinear Differential Equations Analysis · Nonlinear Partial Differential Equations · Stability and Controllability of Differential Equations