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Lipschitz Regularity for Censored Subdiffusive Integro-Differential Equations with Superfractional Gradient Terms

Abstract : In this paper we are interested in integro-differential elliptic and parabolic equations involving nonlocal operators with order less than one, and a gradient term whose coercivity growth makes it the leading term in the equation. We obtain Lipschitz regularity results for the associated stationary Dirichlet problem in the case when the nonlocality of the operator is confined to the domain, feature which is known in the literature as censored nonlocality. As an application of this result, we obtain strong comparison principles which allow us to prove the well-posedness of both the stationary and evolution problems, and steady/ergodic large time behavior for the associated evolution problem.
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https://hal.archives-ouvertes.fr/hal-01081722
Contributor : Guy Barles Connect in order to contact the contributor
Submitted on : Friday, May 8, 2015 - 8:18:01 AM
Last modification on : Thursday, May 12, 2022 - 8:38:02 AM
Long-term archiving on: : Monday, September 14, 2015 - 9:10:38 PM

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  • HAL Id : hal-01081722, version 2
  • ARXIV : 1412.2621

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Guy Barles, Erwin Topp. Lipschitz Regularity for Censored Subdiffusive Integro-Differential Equations with Superfractional Gradient Terms. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2016, 131, pp.3-31. ⟨hal-01081722v2⟩

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