Linear and fully nonlinear elliptic equations with Ld -drift

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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.

Original languageEnglish (US)
JournalCommunications in Partial Differential Equations
StateAccepted/In press - 2020


  • Fully nonlinear equations
  • interior estimates
  • solvability
  • unbounded coefficients

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