Linear and fully nonlinear elliptic equations with Ld  -drift

Nicolai V. Krylov

doi:10.1080/03605302.2020.1805462

Linear and fully nonlinear elliptic equations with L_d -drift

Nicolai V. Krylov

School of Mathematics

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

12 Scopus citations

Abstract

In subdomains of (Formula presented.) we consider uniformly elliptic equations (Formula presented.) with the growth of H with respect to (Formula presented.) controlled by the product of a function from L_d and (Formula presented.) The dependence of H on x is assumed to be of BMO type. Among other things we prove that there exists (Formula presented.) such that for any (Formula presented.) the equation with prescribed continuous boundary data has a solution in class (Formula presented.) Our results are new even if H is linear.

Original language	English (US)
Pages (from-to)	1778-1798
Number of pages	21
Journal	Communications in Partial Differential Equations
Volume	45
Issue number	12
DOIs	https://doi.org/10.1080/03605302.2020.1805462
State	Published - Aug 14 2020

Bibliographical note

Publisher Copyright:
© 2020 Taylor & Francis Group, LLC.

Keywords

Fully nonlinear equations
interior estimates
solvability
unbounded coefficients

Publisher link

10.1080/03605302.2020.1805462

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Cite this

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title = "Linear and fully nonlinear elliptic equations with Ld -drift",

abstract = "In subdomains of (Formula presented.) we consider uniformly elliptic equations (Formula presented.) with the growth of H with respect to (Formula presented.) controlled by the product of a function from Ld and (Formula presented.) The dependence of H on x is assumed to be of BMO type. Among other things we prove that there exists (Formula presented.) such that for any (Formula presented.) the equation with prescribed continuous boundary data has a solution in class (Formula presented.) Our results are new even if H is linear.",

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PY - 2020/8/14

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N2 - In subdomains of (Formula presented.) we consider uniformly elliptic equations (Formula presented.) with the growth of H with respect to (Formula presented.) controlled by the product of a function from Ld and (Formula presented.) The dependence of H on x is assumed to be of BMO type. Among other things we prove that there exists (Formula presented.) such that for any (Formula presented.) the equation with prescribed continuous boundary data has a solution in class (Formula presented.) Our results are new even if H is linear.

AB - In subdomains of (Formula presented.) we consider uniformly elliptic equations (Formula presented.) with the growth of H with respect to (Formula presented.) controlled by the product of a function from Ld and (Formula presented.) The dependence of H on x is assumed to be of BMO type. Among other things we prove that there exists (Formula presented.) such that for any (Formula presented.) the equation with prescribed continuous boundary data has a solution in class (Formula presented.) Our results are new even if H is linear.

KW - Fully nonlinear equations

KW - interior estimates

KW - solvability

KW - unbounded coefficients

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JF - Communications in Partial Differential Equations

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