Comparison principle for unbounded viscosity solutions of degenerate elliptic PDEs with gradient superlinear terms

Shigeaki Koike; Olivier Ley

doi:10.1016/j.jmaa.2011.03.009

Comparison principle for unbounded viscosity solutions of degenerate elliptic PDEs with gradient superlinear terms

Shigeaki Koike^*, Olivier Ley

^*Corresponding author for this work

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

9 Citations (Scopus)

Abstract

We are concerned with fully nonlinear possibly degenerate elliptic partial differential equations (PDEs) with superlinear terms with respect to Du. We prove several comparison principles among viscosity solutions which may be unbounded under some polynomial-type growth conditions. Our main result applies to PDEs with convex superlinear terms but we also obtain some results in nonconvex cases. Applications to monotone systems of PDEs are given.

Original language	English
Pages (from-to)	110-120
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	381
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2011.03.009
Publication status	Published - 2011 Sept 1
Externally published	Yes

Keywords

Comparison principle
Growth conditions
Nonconvex hamiltonians
Systems of pDE
Viscosity solution

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2011.03.009

Cite this

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title = "Comparison principle for unbounded viscosity solutions of degenerate elliptic PDEs with gradient superlinear terms",

abstract = "We are concerned with fully nonlinear possibly degenerate elliptic partial differential equations (PDEs) with superlinear terms with respect to Du. We prove several comparison principles among viscosity solutions which may be unbounded under some polynomial-type growth conditions. Our main result applies to PDEs with convex superlinear terms but we also obtain some results in nonconvex cases. Applications to monotone systems of PDEs are given.",

keywords = "Comparison principle, Growth conditions, Nonconvex hamiltonians, Systems of pDE, Viscosity solution",

author = "Shigeaki Koike and Olivier Ley",

note = "Funding Information: * Corresponding author. E-mail addresses: skoike@rimath.saitama-u.ac.jp (S. Koike), olivier.ley@insa-rennes.fr (O. Ley). 1 S.K. was supported in part by Grant-in-Aid for Scientific Research (No. 20340026) of Japan Society for the Promotion of Science. 2 O.L. is partially supported by ANR BLANC07-3 187245, Hamilton–Jacobi and Weak KAM Theory.",

year = "2011",

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day = "1",

doi = "10.1016/j.jmaa.2011.03.009",

language = "English",

volume = "381",

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journal = "Journal of Mathematical Analysis and Applications",

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T1 - Comparison principle for unbounded viscosity solutions of degenerate elliptic PDEs with gradient superlinear terms

AU - Koike, Shigeaki

AU - Ley, Olivier

N1 - Funding Information: * Corresponding author. E-mail addresses: skoike@rimath.saitama-u.ac.jp (S. Koike), olivier.ley@insa-rennes.fr (O. Ley). 1 S.K. was supported in part by Grant-in-Aid for Scientific Research (No. 20340026) of Japan Society for the Promotion of Science. 2 O.L. is partially supported by ANR BLANC07-3 187245, Hamilton–Jacobi and Weak KAM Theory.

PY - 2011/9/1

Y1 - 2011/9/1

N2 - We are concerned with fully nonlinear possibly degenerate elliptic partial differential equations (PDEs) with superlinear terms with respect to Du. We prove several comparison principles among viscosity solutions which may be unbounded under some polynomial-type growth conditions. Our main result applies to PDEs with convex superlinear terms but we also obtain some results in nonconvex cases. Applications to monotone systems of PDEs are given.

AB - We are concerned with fully nonlinear possibly degenerate elliptic partial differential equations (PDEs) with superlinear terms with respect to Du. We prove several comparison principles among viscosity solutions which may be unbounded under some polynomial-type growth conditions. Our main result applies to PDEs with convex superlinear terms but we also obtain some results in nonconvex cases. Applications to monotone systems of PDEs are given.

KW - Comparison principle

KW - Growth conditions

KW - Nonconvex hamiltonians

KW - Systems of pDE

KW - Viscosity solution

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DO - 10.1016/j.jmaa.2011.03.009

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AN - SCOPUS:79955478545

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Comparison principle for unbounded viscosity solutions of degenerate elliptic PDEs with gradient superlinear terms

Abstract

Keywords

ASJC Scopus subject areas

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