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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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##### References:
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