Linear and fully nonlinear elliptic equations with <i>L<sub>d</sub></i>-drift
Н. В. Крылов
Abstract
In subdomains of Rd, we consider uniformly elliptic equations H(v(x),Dv(x),D2v(x),x)=0 with the growth of H with respect to |Dv| controlled by the product of a function from Ld and |Dv|. The dependence of H on x is assumed to be of BMO type. Among other things we prove that there exists d0∈(d/2,d) such that for any p∈(d0,d) the equation with prescribed continuous boundary data has a solution in class Wp,loc2. Our results are new even if H is linear.
Topics & Concepts
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