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,W-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.

Adamowicz, T., Veronelli, G. (2024). Isoperimetric inequalities and regularity of A-harmonic functions on surfaces. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 63(2) [10.1007/s00526-023-02651-y].

Isoperimetric inequalities and regularity of A-harmonic functions on surfaces

Veronelli G.
2024

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,W-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.
Articolo in rivista - Articolo scientifico
Riemannian surfaces, p-harmonic functions, isoperimetric inequalities, minimal graphs
English
28-gen-2024
2024
63
2
48
partially_open
Adamowicz, T., Veronelli, G. (2024). Isoperimetric inequalities and regularity of A-harmonic functions on surfaces. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 63(2) [10.1007/s00526-023-02651-y].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/476103
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