We investigate elementary properties of a Finsler-Laplacian operator Q that is associated with functionals containing (H(Delta u))^2. Here H is convex and homogeneous of degree 1, and its polar H^o represents a Finsler metric on R^n. In particular we study the Dirichlet problem -Qu = 2n on a ball K^o = {x is an element of R^n : H^o(x) < 1} and present a fundamental solution for Q, suitable maximum and comparison principles, and a mean value property for solutions of Qu = 0.
Remarks on a Finsler-Laplacian / Ferone, Vincenzo; B., Kawohl. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 137:1(2009), pp. 247-253.
Remarks on a Finsler-Laplacian
FERONE, VINCENZO;
2009
Abstract
We investigate elementary properties of a Finsler-Laplacian operator Q that is associated with functionals containing (H(Delta u))^2. Here H is convex and homogeneous of degree 1, and its polar H^o represents a Finsler metric on R^n. In particular we study the Dirichlet problem -Qu = 2n on a ball K^o = {x is an element of R^n : H^o(x) < 1} and present a fundamental solution for Q, suitable maximum and comparison principles, and a mean value property for solutions of Qu = 0.| File | Dimensione | Formato | |
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