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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Remarks on a Finsler-Laplacian


Authors: Vincenzo Ferone and Bernd Kawohl
Journal: Proc. Amer. Math. Soc. 137 (2009), 247-253
MSC (2000): Primary 35J60, 53C60, 49Q20
Published electronically: August 15, 2008
MathSciNet review: 2439447
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Abstract: We investigate elementary properties of a Finsler-Laplacian operator $ Q$ that is associated with functionals containing $ (H(\nabla u))^2$. Here $ H$ is convex and homogeneous of degree 1, and its polar $ H^o$ represents a Finsler metric on $ \mathbb{R}^n$. In particular we study the Dirichlet problem $ -Qu=2n$ on a ball $ K^o=\{x\in\mathbb{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$.


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Additional Information

Vincenzo Ferone
Affiliation: Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico II”, Complesso Universitario Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy
Email: ferone@unina.it

Bernd Kawohl
Affiliation: Mathematisches Institut, Universität zu Köln, D-50923 Köln, Germany
Email: kawohl@mi.uni-koeln.de

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09554-3
PII: S 0002-9939(08)09554-3
Received by editor(s): January 15, 2008
Published electronically: August 15, 2008
Communicated by: Walter Craig
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.