Moser-Trudinger and logarithmic HLS inequalities for systems

• Autores: Gershon Wolansky, Itai Shafrir
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 7, Nº 4, 2005, págs. 413-448
• Idioma: inglés
• DOI: 10.4171/jems/34
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• Resumen

  • We prove several optimal Moser-Trudinger and logarithmic Hardy-Littlewood-Sobolev inequalities for systems in two dimensions. These include inequalities on the sphere $S2$, on a bounded domain $\Omega\subset\R2$ and on all of $\R2$. In some cases we also address the question of existence of minimizers.