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Perron's method for
nonlocal fully nonlinear equations
Chenchen Mou |
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Vol. 10 (2017), No. 5, 1227–1254
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Abstract |
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This paper is concerned with the existence of viscosity solutions of nonlocal fully nonlinear equations that are not translation-invariant. We construct a discontinuous viscosity solution of such a nonlocal equation by Perron’s method. If the equation is uniformly elliptic, we prove the discontinuous viscosity solution is Hölder continuous and thus it is a viscosity solution. |
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Keywords
viscosity solution, integro-PDE,
Hamilton–Jacobi–Bellman–Isaacs
equation, Perron's method, weak Harnack inequality
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Mathematical Subject Classification 2010
Primary: 35D40, 35J60, 35R09, 47G20, 49N70
Secondary: 45K05
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Milestones
Received: 24 November 2016
Revised: 1 February 2017
Accepted: 24 April 2017
Published: 1 July 2017
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Authors |
| Chenchen Mou | |
| Department of Mathematics UCLA Los Angeles, CA 90095 United States |
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