List questions from elliptic-equations

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List Question

Dirichlet Problem: symmetry of the solution with respect to the $x_1$ variable

The averages of a subharmonic function over concentric balls increase with radius

Some questions about function's growth.

An exercise in the chapter of elliptic equations in Evans's PDE

The Poisson equation with $L^2$ data has a unique weak solution in $H^1$

Problem 5 of chapter 6 of Evans PDE 1st.

Precise analysis of physical interpretations of elliptic

Proof of the Hopf Lemma for Elliptic Equations.

Second order elliptic equation with nonlinearity depending on the gradient

Potential theory solution for Variable coefficient Poisson with Dirichlet Boundary conditions

Calculus of variations - existence of minimum of a functional-elliptic problem

about lower semicontinuity of a functional - PDE

Galerkin method in Sobolev space

Is this element of $H^1(\Omega)^*$ actually in $L^2(\Omega)$?

Is this statement about the solution to an elliptic problem true.

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