| Abstract: |
| We consider the Dirichlet problem for second-order elliptic equations in non-divergence form $L$ and double divergence form $L^*$. We introduce a potential theory framework for these operators, including Perron`s method, capacity theory, and Wiener`s criterion. We establish the equivalence between regular boundary points for these operators $L$ and $L^*$ with those for the Laplace operator, assuming that the principal coefficients satisfy the Dini mean oscillation condition. |
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