Elliptic and Parabolic Equations - Abstract

Stara, Jana

Regularity results for the gradient of solutions of linear elliptic systems with VMO coefficients and $L^1,lambda$ data

We prove that if a vector function $f$ belongs to Morrey space $L^1,lambda(Omega, Bbb R^N)$ with smoothly bounded $Omega subset Bbb R^n$ for $n geq 3, Ngeq 2, lambda in [0,n-2]$ then there exists a very weak solution $u in W^1,1(Omega,Bbb R^N)$ to linear elliptic boundary value problem begineqnarray mathcal A(u) equiv - mathrmdiv(A Du) = f mathrmon Omega nonumber
u = 0 mathrmon partialOmega nonumber endeqnarray noindent such that $Du in L_loc^q, n - q(n-lambda -1)(Omega, Bbb R^N)$ for any $q in [1,fracnn-1)$ provided the coefficient matrix $A$ has $L^infty(Omega)cap VMO(Omega)$ entries.