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On general solvability properties of \(p\)-Laplacian-like equations. (English) Zbl 1030.35058

Summary: 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 \(\Omega = \mathbb R ^N\).

MSC:

35J60 Nonlinear elliptic equations
35J20 Variational methods for second-order elliptic equations
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