Existence and non-existence of minimizers for Poincar 'e-Sobolev\n inequalities

2018/10/12 by Rafael D. Benguria, Benguria, Rafael D., Cristóbal Vallejos +3
Mathematics · #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1810.05698

Abstract

In this paper we study the existence and non-existence of minimizers for a\ntype of (critical) Poincar 'e-Sobolev inequalities. We show that minimizers\ndo exist for smooth domains in \ℝ^d, an also for some polyhedral\ndomains. On the other hand, we prove the non-existence of minimizers in the\nrectangular isosceles triangle in \ℝ².\n

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