An extension problem for sums of fractional Laplacians and 1-D symmetry of phase transitions
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hdl:2117/85537
Tipus de documentArticle
Data publicació2015-09-10
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Abstract
We study nonlinear elliptic equations for operators corresponding to non-stable Lévy diffusions. We include a sum of fractional Laplacians of different orders. Such operators are infinitesimal generators of non-stable (i.e., non self-similar) Lévy processes. We establish the regularity of solutions, as well as sharp energy estimates. As a consequence, we prove a 1-D symmetry result for monotone solutions to Allen-Cahn type equations with a non-stable Lévy diffusion. These operators may still be realized as local operators using a system of PDEs - in the spirit of the extension problem of Caffarelli and Silvestre.
CitacióCabre, X., Serra, J. An extension problem for sums of fractional Laplacians and 1-D symmetry of phase transitions. "Nonlinear analysis, theory, methods and applications", May 2016, Vol. 137, p.246-265
ISSN0362-546X
Versió de l'editorhttp://www.sciencedirect.com/science/article/pii/S0362546X15004307
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