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quasilinear elliptic equations; weak solutions; solvability
We discuss how the choice of the functional setting and the definition of the weak solution affect the existence and uniqueness of the solution to the equation \[ -\Delta _p u = f \ \text{in} \ \Omega , \] where $\Omega $ is a very general domain in $\mathbb{R}^N$, including the case $\Omega = \mathbb{R}^N$.
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