On equations of minimax type in the theory of elliptic and parabolic equations in the plane

N. V. Krylov

doi:10.1070/SM1970v010n01ABEH002151

On equations of minimax type in the theory of elliptic and parabolic equations in the plane

N. V. Krylov

Mathematics

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

6 Scopus citations

Abstract

The existence and uniqueness of the solution in Sobolev spaces W²_p(W^{2, 1}_p) is proved for the first boundary value problem for elliptic (parabolic) equations of the form (formula presented)Here (formula presented) and (formula presented) in the elliptic case, (formula presented) Parabolic case. The subscript p takes any values close to two.

Original language	English (US)
Pages (from-to)	1-19
Number of pages	19
Journal	Mathematics of the USSR - Sbornik
Volume	10
Issue number	1
DOIs	https://doi.org/10.1070/SM1970v010n01ABEH002151
State	Published - Feb 28 1970

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abstract = "The existence and uniqueness of the solution in Sobolev spaces W2p(W2, 1p) is proved for the first boundary value problem for elliptic (parabolic) equations of the form (formula presented)Here (formula presented) and (formula presented) in the elliptic case, (formula presented) Parabolic case. The subscript p takes any values close to two.",

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AB - The existence and uniqueness of the solution in Sobolev spaces W2p(W2, 1p) is proved for the first boundary value problem for elliptic (parabolic) equations of the form (formula presented)Here (formula presented) and (formula presented) in the elliptic case, (formula presented) Parabolic case. The subscript p takes any values close to two.

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On equations of minimax type in the theory of elliptic and parabolic equations in the plane

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