Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations
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...
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Texas State University
1999-07-01
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Series: | Electronic Journal of Differential Equations |
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Online Access: | http://ejde.math.txstate.edu/Volumes/1999/24/abstr.html |
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doaj-0df6242703634ad0a4556e6738c776582020-11-24T20:58:50ZengTexas State UniversityElectronic Journal of Differential Equations1072-66911999-07-01199924120Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equationsM. G. CrandallM. KocanP. L. LionsA. SwiechWe 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. http://ejde.math.txstate.edu/Volumes/1999/24/abstr.htmlUniformly elliptic and parabolic equationsviscosity solutionsgood solutionsexterior cone conditionbarrier functions. |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
M. G. Crandall M. Kocan P. L. Lions A. Swiech |
spellingShingle |
M. G. Crandall M. Kocan P. L. Lions A. Swiech Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations Electronic Journal of Differential Equations Uniformly elliptic and parabolic equations viscosity solutions good solutions exterior cone condition barrier functions. |
author_facet |
M. G. Crandall M. Kocan P. L. Lions A. Swiech |
author_sort |
M. G. Crandall |
title |
Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations |
title_short |
Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations |
title_full |
Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations |
title_fullStr |
Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations |
title_full_unstemmed |
Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations |
title_sort |
existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations |
publisher |
Texas State University |
series |
Electronic Journal of Differential Equations |
issn |
1072-6691 |
publishDate |
1999-07-01 |
description |
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. |
topic |
Uniformly elliptic and parabolic equations viscosity solutions good solutions exterior cone condition barrier functions. |
url |
http://ejde.math.txstate.edu/Volumes/1999/24/abstr.html |
work_keys_str_mv |
AT mgcrandall existenceresultsforboundaryproblemsforuniformlyellipticandparabolicfullynonlinearequations AT mkocan existenceresultsforboundaryproblemsforuniformlyellipticandparabolicfullynonlinearequations AT pllions existenceresultsforboundaryproblemsforuniformlyellipticandparabolicfullynonlinearequations AT aswiech existenceresultsforboundaryproblemsforuniformlyellipticandparabolicfullynonlinearequations |
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1716784374673833984 |