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## Details

Document Type: | Book |
---|---|

All Authors / Contributors: |
N V Krylov |

ISBN: | 9781470447403 1470447401 |

OCLC Number: | 1039672482 |

Notes: | "Applied mathematics"--Cover. |

Description: | xiv, 441 pages ; 27 cm. |

Contents: | Bellman's equations with constant ``coefficients'' in the whole spaceEstimates in $L_p$ for solutions of the Monge-Ampere type equationsThe Aleksandrov estimatesFirst results for fully nonlinear equationsFinite-difference equations of elliptic typeElliptic differential equations of cut-off typeFinite-difference equations of parabolic typeParabolic differential equations of cut-off typeA priori estimates in $C^\alpha$ for solutions of linear and nonlinear equationsSolvability in $W^2_{p,\mathrm{loc}}$ of fully nonlinear elliptic equationsNonlinear elliptic equations in $C^{2+\alpha}_{\mathrm{loc}}(\Omega)\cap C(\overline{\Omega})$Solvability in $W^{1,2}_{p,\mathrm{loc}}$ of fully nonlinear parabolic equationsElements of the $C^{2+\alpha}$-theory of fully nonlinear elliptic and parabolic equationsNonlinear elliptic equations in $W^2_p(\Omega)$Nonlinear parabolic equations in $W^{1,2}_p$$C^{1+\alpha}$-regularity of viscosity solutions of general parabolic equations$C^{1+\alpha}$-regularity of $L_p$-viscosity solutions of the Isaacs parabolic equations with almost VMO coefficientsUniqueness and existence of extremal viscosity solutions for parabolic equationsAppendix A. Proof of Theorem 6.2.1Appendix B. Proof of Lemma 9.2.6Appendix C. Some tools from real analysisBibliographyIndex |

Series Title: | Mathematical surveys and monographs, no. 233. |

Responsibility: | N.V. Krylov. |

### Abstract:

Concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. The authors look for solutions in Sobolev classes, or for viscosity solutions. Most of the auxiliary results are taken from old sources, and the main results were obtained in the last few years.
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## Similar Items

### Related Subjects:(6)

- Viscosity solutions.
- Elliptic functions.
- Differential equations, Parabolic.
- Partial differential equations -- Research exposition (monographs, survey articles)
- Partial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations.
- Partial differential equations -- Parabolic equations and systems -- Nonlinear parabolic equations.