In this paper we consider semilinear elliptic systems of differential inequalities in the whole Euclidean space in dimension greater or equal two. We investigate the threshold between existence and non-existence of solutions in a suitable weak sense and without positiveness conditions. We obtain a sharp non-existence result relying on the method of nonlinear capacity estimates.
Remarks on a “Serrin curve” for systems of differential inequalities / D. Cassani. - In: RENDICONTI. CLASSE DI SCIENZE MATEMATICHE E NATURALI. - ISSN 1974-6989. - 140:(2009), pp. 113-124.
Remarks on a “Serrin curve” for systems of differential inequalities
D. CassaniPrimo
2009
Abstract
In this paper we consider semilinear elliptic systems of differential inequalities in the whole Euclidean space in dimension greater or equal two. We investigate the threshold between existence and non-existence of solutions in a suitable weak sense and without positiveness conditions. We obtain a sharp non-existence result relying on the method of nonlinear capacity estimates.
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