On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains (Q2849047)
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scientific article; zbMATH DE number 6208257
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains |
scientific article; zbMATH DE number 6208257 |
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On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains (English)
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16 September 2013
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vanishing mean oscillation
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Bellman's equations
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The paper is devoted to fully nonlinear elliptic and parabolic equations with vanishing mean oscillation coefficients in bounded domains or cylinders. The systems under consideration particularly cover parabolic Bellman's equations. The solvability in the Sobolev spaces of the terminal-boundary value problem is proved. The solvability in \(W^{1,2}_p\), \(p>d+1\), of the corresponding elliptic boundary value problem is also obtained. The proofs of main propositions of the paper are based on the approach developed in works by the second author [Commun. Partial Differ. Equations 32, No. 3, 453--475 (2007; Zbl 1114.35079); J. Funct. Anal. 250, No. 2, 521--558 (2007; Zbl 1133.35052)].
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