Existence of solutions and regularity near the characteristic boundary for sub-Laplacian equations on Carnot groups

• Autores: Dimiter Vassilev
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 227, Nº 2, 2006, pág. 361
• Idioma: inglés
• DOI: 10.2140/pjm.2006.227.361
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• Resumen

  • We prove that the best constant in the Folland¿Stein embedding theorem on Carnot groups is achieved. This implies the existence of a positive solution of the Yamabe-type equation on Carnot groups. The second goal of the paper is to show a certain regularity of the Green¿s function and solutions of the Yamabe equation involving the sub-Laplacian near the characteristic boundary of a domain in the considered groups.