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A generalization of a theorem of H.Brezis & F.E.Browder and applications to some unilateral problems. (English) Zbl 0716.46032
Author’s abstract: The first section of this paper is devoted to prove the following theorem, which extends previous results of H. Brezis and F. E. Browder:
Let \(w\in W_ 0^{m,p}(\Omega)\), \(w\geq 0\) a.e. in \(\Omega\) and \(T\in W^{-m,p'}(\Omega)\), \(T=\mu +h\) where \(\mu\) is a positive Radon measure and \(h\in L^ 1_{loc}(\Omega)\) is such that hw\(\geq -| \phi |\) a.e. in \(\Omega\) for some \(\phi \in L^ 1(\Omega)\); then w belongs to \(L^ 1(\Omega;d\mu)\), hw belongs to \(L^ 1(\Omega)\) and \[ <T,w>=\int_{\Omega}w d\mu +\int_{\Omega}hw dx. \] The second and third sections deal with applications of this theorem to the study of two unilateral problems.
Reviewer: F.Sukochev

MSC:
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
49J40 Variational inequalities
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