Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations

M. G. Crandall; M. Kocan; P. L. Lions; A. Świȩch

Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations

M. G. Crandall^*, M. Kocan, P. L. Lions, A. Świȩch

^*Corresponding author for this work

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

63 Citations (Scopus)

Abstract

We study existence of continuous weak (viscosity) solutions of Dirichlet and Cauchy-Dirichlet problems for fully nonlinear uniformly elliptic and parabolic equations. Two types of results are obtained in contexts where uniqueness of solutions fails or is unknown. For equations with merely measurable coefficients we prove solvability of the problem, while in the continuous case we construct maximal and minimal solutions. Necessary barriers on external cones are also constructed.

Original language	English
Pages (from-to)	1-20
Number of pages	20
Journal	Electronic Journal of Differential Equations
Volume	1999
Publication status	Published - 1 Jul 1999
Externally published	Yes

Cite this

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title = "Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations",

abstract = "We study existence of continuous weak (viscosity) solutions of Dirichlet and Cauchy-Dirichlet problems for fully nonlinear uniformly elliptic and parabolic equations. Two types of results are obtained in contexts where uniqueness of solutions fails or is unknown. For equations with merely measurable coefficients we prove solvability of the problem, while in the continuous case we construct maximal and minimal solutions. Necessary barriers on external cones are also constructed.",

keywords = "Barrier functions, Exterior cone condition, Good solutions, Uniformly elliptic and parabolic equations, Viscosity solutions",

author = "Crandall, {M. G.} and M. Kocan and Lions, {P. L.} and A. {\'S}wiȩch",

year = "1999",

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journal = "Electronic Journal of Differential Equations",

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AU - Crandall, M. G.

AU - Kocan, M.

AU - Lions, P. L.

AU - Świȩch, A.

PY - 1999/7/1

Y1 - 1999/7/1

N2 - We study existence of continuous weak (viscosity) solutions of Dirichlet and Cauchy-Dirichlet problems for fully nonlinear uniformly elliptic and parabolic equations. Two types of results are obtained in contexts where uniqueness of solutions fails or is unknown. For equations with merely measurable coefficients we prove solvability of the problem, while in the continuous case we construct maximal and minimal solutions. Necessary barriers on external cones are also constructed.

AB - We study existence of continuous weak (viscosity) solutions of Dirichlet and Cauchy-Dirichlet problems for fully nonlinear uniformly elliptic and parabolic equations. Two types of results are obtained in contexts where uniqueness of solutions fails or is unknown. For equations with merely measurable coefficients we prove solvability of the problem, while in the continuous case we construct maximal and minimal solutions. Necessary barriers on external cones are also constructed.

KW - Barrier functions

KW - Exterior cone condition

KW - Good solutions

KW - Uniformly elliptic and parabolic equations

KW - Viscosity solutions

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M3 - Article

SN - 1072-6691

VL - 1999

SP - 1

EP - 20

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

ER -

Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations

Abstract

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