\(p\)-Laplacian boundary value problems on exterior regions. (English) Zbl 1332.35101
Summary: This paper treats some variational principles for solutions of inhomogeneous \(p\)-Laplacian boundary value problems on exterior regions \(U\subsetneq\mathbb R^N\) with dimension \(N\geq 3\). Existence-uniqueness results when \(p\in(1,N)\) are provided in a space \(E^{1,p}(U)\) of functions that contains \(W^{1,p}(U)\). Functions in \(E^{1,p}(U)\) are required to decay at infinity in a measure theoretic sense. Various properties of this space are derived, including results about equivalent norms, traces and an \(L^p\)-imbedding theorem. Also an existence result for a general variational problem of this type is obtained.
MSC:
| 35J35 | Variational methods for higher-order elliptic equations |
| 35J40 | Boundary value problems for higher-order elliptic equations |
| 35A15 | Variational methods applied to PDEs |
Keywords:
exterior regions; \(p\)-Laplacian boundary value problems; variational principles; energy spacesReferences:
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