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Problemi e convergenze variazionali su domini non limitati

Summary

We introduce a class of second order elliptic operators from H 0 1 (Ω) to his dual space H−1(Ω), where Ω is an open set in Rn that we allow to be unbounded. We prove that such operators are continuously invertible and that the constant majoryzing the norm of their inverses depends only on the parameters of the class. We prove moreover that if T ε H−1(Ω) is given then the set of the L−1T, where L belongs to the mentioned class is relatively compact in L2(Ω). Next we study the relationships between several kinds of convergence (one of them is the G-convergence) and we study in what cases the spectrum function is semicontinuous or continuous on certain subsets of our class of operators.

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Bottaro, G., Oppezzi, P. Problemi e convergenze variazionali su domini non limitati. Annali di Matematica pura ed applicata 151, 247–261 (1988). https://doi.org/10.1007/BF01762798

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