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

Lions, Pierre-Louis; Kocan, Maciej; Crandall, Michael G.; Swiech, Andrzej (1999), Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations, Electronic Journal of Differential Equations, 1999, 24, p. 1-20

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Type
Article accepté pour publication ou publié
Date
1999
Journal name
Electronic Journal of Differential Equations
Volume
1999
Number
24
Publisher
Texas State University
Pages
1-20
Metadata
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Author(s)
Lions, Pierre-Louis
Kocan, Maciej
Crandall, Michael G.
Swiech, Andrzej
Abstract (EN)
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.
Subjects / Keywords
barrier functions; exterior cone condition; good solutions; viscosity solutions; Uniformly elliptic and parabolic equations