A theorem on degenerrate elliptic Beliman equation in bounded domains

N. V. Krylov; L. A. Caffarelli

A theorem on degenerrate elliptic Beliman equation in bounded domains

N. V. Krylov, L. A. Caffarelli

School of Mathematics

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

2 Scopus citations

Abstract

A general existence and uniqueness theorem for degenerate elliptic Bellman equations in bounded domains is proved. Functional classes C^2+α(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) = c_k(x)P_k(u_xx), where P_k(u_xx) is the kth elementary symmetric polynomial of eigenvalues of the matrix u_xx are particular cases of equations under consideration.

Original language	English (US)
Pages (from-to)	1-20
Number of pages	20
Journal	Differential and Integral Equations
Volume	8
Issue number	5
State	Published - May 1995

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title = "A theorem on degenerrate elliptic Beliman equation in bounded domains",

abstract = "A general existence and uniqueness theorem for degenerate elliptic Bellman equations in bounded domains is proved. Functional classes C2+α(D) and C1, 1(D) are the classes where solutions are looked for. This theorem has a very broad range of applicability. Equations ut = uxx and Pm(uxx) = ck(x)Pk(uxx), where Pk(uxx) is the kth elementary symmetric polynomial of eigenvalues of the matrix uxx are particular cases of equations under consideration.",

author = "Krylov, {N. V.} and Caffarelli, {L. A.}",

year = "1995",

month = may,

language = "English (US)",

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journal = "Differential and Integral Equations",

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T1 - A theorem on degenerrate elliptic Beliman equation in bounded domains

AU - Krylov, N. V.

AU - Caffarelli, L. A.

PY - 1995/5

Y1 - 1995/5

N2 - A general existence and uniqueness theorem for degenerate elliptic Bellman equations in bounded domains is proved. Functional classes C2+α(D) and C1, 1(D) are the classes where solutions are looked for. This theorem has a very broad range of applicability. Equations ut = uxx and Pm(uxx) = ck(x)Pk(uxx), where Pk(uxx) is the kth elementary symmetric polynomial of eigenvalues of the matrix uxx are particular cases of equations under consideration.

AB - A general existence and uniqueness theorem for degenerate elliptic Bellman equations in bounded domains is proved. Functional classes C2+α(D) and C1, 1(D) are the classes where solutions are looked for. This theorem has a very broad range of applicability. Equations ut = uxx and Pm(uxx) = ck(x)Pk(uxx), where Pk(uxx) is the kth elementary symmetric polynomial of eigenvalues of the matrix uxx are particular cases of equations under consideration.

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M3 - Article

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JO - Differential and Integral Equations

JF - Differential and Integral Equations

IS - 5

ER -

A theorem on degenerrate elliptic Beliman equation in bounded domains

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