Regularity results and large time behavior for integro-differential equations with coercive Hamiltonians
Author
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Barles, Guy
Author
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Koike, Shigeaki
es_CL
Author
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Ley, Olivier
es_CL
Author
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Topp Paredes, Erwin
es_CL
Admission date
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2014-12-10T20:31:34Z
Available date
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2014-12-10T20:31:34Z
Publication date
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2014
Cita de ítem
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Calculus of Variations (2015) 54:539–572
Identifier
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DOI 10.1007/s00526-014-0794-x
Identifier
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https://repositorio.uchile.cl/handle/2250/126505
General note
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Articulo de publicacion SCOPUS
en_US
Abstract
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In this paper we obtain regularity results for elliptic integro-differential equations
driven by the stronger effect of coercive gradient terms. This feature allows us to construct
suitable strict supersolutions from which we conclude Hölder estimates for bounded subsolutions.
In many interesting situations, this gives way to a priori estimates for subsolutions.
We apply this regularity results to obtain the ergodic asymptotic behavior of the associated
evolution problem in the case of superlinear equations. One of the surprising features in our
proof is that it avoids the key ingredient which are usually necessary to use the strong maximum
principle: linearization based on the Lipschitz regularity of the solution of the ergodic
problem. The proof entirely relies on the Hölder regularity.
en_US
Patrocinador
dc.description.sponsorship
ANR (Agence Nationale de la Recherche)
Japan Society for the Promotion of Science.
Grants
Capital Humano Avanzado, Cotutela en el Extranjero