• Where can I find a reference on the following anisotropic problem? $$(\bullet) \qquad \begin{align*} \nabla_x (A(x) \nabla_x u(x,y)) + \Delta_y(K(y) \ast u(x,y))\end{align*}=0, $$ where $(x,y) \in \mathbb{R}^{N_1}\times \mathbb{R}^{N_2}$, and $K$ is some (not necessarily smooth) "convolution kernel" and $A$ is uniformly elliptic.

  • What are other references problems with anisotropies similar or related to $(\bullet)$? That is problems with different (possibly nonlocal) ellipticity coefficients for the space variables $(x,y) \in \mathbb{R}^{N_1}\times \mathbb{R}^{N_2}$.


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