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- Title
Isoperimetric inequalities and regularity of A-harmonic functions on surfaces.
- Authors
Adamowicz, Tomasz; Veronelli, Giona
- Abstract
We investigate the logarithmic and power-type convexity of the length of the level curves for a-harmonic functions on smooth surfaces and related isoperimetric inequalities. In particular, our analysis covers the p-harmonic and the minimal surface equations. As an auxiliary result, we obtain higher Sobolev regularity properties of the solutions, including the W 2 , 2 regularity. The results are complemented by a number of estimates for the derivatives L ′ and L ′ ′ of the length of the level curve function L, as well as by examples illustrating the presentation. Our work generalizes results due to Alessandrini, Longinetti, Talenti and Lewis in the Euclidean setting, as well as a recent article of ours devoted to the harmonic case on surfaces.
- Subjects
ISOPERIMETRIC inequalities; MINIMAL surfaces; SMOOTHNESS of functions; EQUATIONS
- Publication
Calculus of Variations & Partial Differential Equations, 2024, Vol 63, Issue 2, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-023-02651-y