Some remarks on Sobolev type inequalities

Adimurthi, ; Yadava, S. L. (1994) Some remarks on Sobolev type inequalities Calculus of Variations and Partial Differential Equations, 2 (4). pp. 427-442. ISSN 0944-2669

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We extend two Sobolev type inequalities for balls to arbitrary smooth bounded domains. In the case of balls, one inequality is due to Brezis and Lieb and another is due to Escobar. The extension has been achieved by analyzing the asymptotic behaviour of solutions of certain semilinear Neumann problems.

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