Existence of strong solutions of Pucci extremal equations with superlinear growth in Du

Shigeaki Koike; Andrzej Święch

doi:10.1007/s11784-009-0106-9

Existence of strong solutions of Pucci extremal equations with superlinear growth in Du

Shigeaki Koike, Andrzej Święch

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

We prove existence of strong solutions of Pucci extremal equations with superlinear growth in Du and unbounded coefficients. We apply this result to establish the weak Harnack inequality for L ^p -viscosity supersolutions of fully nonlinear uniformly elliptic PDEs with superlinear growth terms with respect to Du.

Original language	English
Pages (from-to)	291-304
Number of pages	14
Journal	Journal of Fixed Point Theory and Applications
Volume	5
Issue number	2
DOIs	https://doi.org/10.1007/s11784-009-0106-9
Publication status	Published - 2009 Aug

Keywords

Pucci extremal equation
Strong solutions
Viscosity solutions
Weak Harnack inequality

ASJC Scopus subject areas

Modelling and Simulation
Geometry and Topology
Applied Mathematics

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10.1007/s11784-009-0106-9

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title = "Existence of strong solutions of Pucci extremal equations with superlinear growth in Du",

abstract = " We prove existence of strong solutions of Pucci extremal equations with superlinear growth in Du and unbounded coefficients. We apply this result to establish the weak Harnack inequality for L p -viscosity supersolutions of fully nonlinear uniformly elliptic PDEs with superlinear growth terms with respect to Du.",

keywords = "Pucci extremal equation, Strong solutions, Viscosity solutions, Weak Harnack inequality",

author = "Shigeaki Koike and Andrzej {\'S}wi{\c e}ch",

note = "Funding Information: S. Koike was supported by Grant-in-Aid for Scientific Research (No. 20340026) of Japan Society for the Promotion of Science. A. {\'S}wi{\c e}ch was supported by NSF grant DMS 0500270. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",

year = "2009",

month = aug,

doi = "10.1007/s11784-009-0106-9",

language = "English",

volume = "5",

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journal = "Journal of Fixed Point Theory and Applications",

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T1 - Existence of strong solutions of Pucci extremal equations with superlinear growth in Du

AU - Koike, Shigeaki

AU - Święch, Andrzej

N1 - Funding Information: S. Koike was supported by Grant-in-Aid for Scientific Research (No. 20340026) of Japan Society for the Promotion of Science. A. Święch was supported by NSF grant DMS 0500270. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2009/8

Y1 - 2009/8

N2 - We prove existence of strong solutions of Pucci extremal equations with superlinear growth in Du and unbounded coefficients. We apply this result to establish the weak Harnack inequality for L p -viscosity supersolutions of fully nonlinear uniformly elliptic PDEs with superlinear growth terms with respect to Du.

AB - We prove existence of strong solutions of Pucci extremal equations with superlinear growth in Du and unbounded coefficients. We apply this result to establish the weak Harnack inequality for L p -viscosity supersolutions of fully nonlinear uniformly elliptic PDEs with superlinear growth terms with respect to Du.

KW - Pucci extremal equation

KW - Strong solutions

KW - Viscosity solutions

KW - Weak Harnack inequality

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SN - 1661-7738

IS - 2

ER -

Existence of strong solutions of Pucci extremal equations with superlinear growth in Du

Abstract

Keywords

ASJC Scopus subject areas

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