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1995 A theorem on degenerate elliptic Bellman equations in bounded domains
N. V. Krylov
Differential Integral Equations 8(5): 961-980 (1995).

Abstract

A general existence and uniqueness theorem for degenerate elliptic Bellman equations in bounded domains is proved. Functional classes $C^{2+\alpha}(D)$ and $C^{1,1}(D)$ are the classes where solutions are looked for. This theorem has a very broad range of applicability. Equations $u_{t}=u_{xx}$ and $$ P_{m}(u_{xx})=\sum_{k=0}^{m-1}c_{k}(x)P_{k}(u_{xx}), $$ where $P_{k}(u_{xx})$ is the $k$th elementary symmetric polynomial of eigenvalues of the matrix $u_{xx}$ are particular cases of equations under consideration.

Citation

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N. V. Krylov. "A theorem on degenerate elliptic Bellman equations in bounded domains." Differential Integral Equations 8 (5) 961 - 980, 1995.

Information

Published: 1995
First available in Project Euclid: 20 May 2013

zbMATH: 0880.35042
MathSciNet: MR1325541

Subjects:
Primary: 35J70

Rights: Copyright © 1995 Khayyam Publishing, Inc.

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Vol.8 • No. 5 • 1995
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