The ๐ฟ^{๐} Dirichlet problem and nondivergence harmonic measure
Cristian Rios ยท Transactions of the American Mathematical Society ยท 2002
We consider the Dirichlet problem \[ { L u a m p ; = 0 a m p ; a m p ; in D , u a m p ; = g a m p ; a m p ; on โ D \left \{ \begin {aligned} \mathcal {L} u & = 0 &&\text {in $D$},\\ u &= g &&\text {on $\partial D$} \end {aligned} \right . \] for two second-order elliptic operators L k u = โ i , j = 1 n a k i , j ( x ) โ i j u ( x ) \mathcal {L}_k u=\sum _{i,j=1}^na_k^{i,j}(x)\,\partial _{ij} u(x) , k = 0 , 1 k=0,1 , in a bounded Lipschitz domain D โ R n