Existence of Cα solutions to integro-PDEs

This paper is concerned with existence of a C α viscosity solution of a second order non-translation invariant integro-PDE. We first obtain a weak Harnack inequality for such integro-PDE. We then use the weak Harnack inequality to prove Hölder regularity and existence of solutions of the integro-PDE...

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Bibliographic Details
Published inCalculus of variations and partial differential equations Vol. 58; no. 4; pp. 1 - 28
Main Author Mou, Chenchen
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 2019
Springer Nature B.V
Subjects
Analysis
Calculus of Variations and Optimal Control; Optimization
Control
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
35R09
35D40
45K05
47G20
35J60
49N70
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Summary:This paper is concerned with existence of a C α viscosity solution of a second order non-translation invariant integro-PDE. We first obtain a weak Harnack inequality for such integro-PDE. We then use the weak Harnack inequality to prove Hölder regularity and existence of solutions of the integro-PDEs.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-019-1597-x