W1,1 0 (Ω)-solutions for some elliptic systems with a convection term and principal part not uniformly elliptic

• Lucio Boccardo ^[1]
  1. [1] Istituto Lombardo, Sapienza Università di Roma
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 83, Nº. 3, 2026, págs. 597-605
• Idioma: inglés
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• Resumen

  • In this paper, we study the existence of solutions of an elliptic system with one of the two principal parts not uniformly elliptic; there are cases of W1,2 0 (Ω) solutions and there are cases of W1,1 0 (Ω) solutions: despite the L1 estimate on the gradient, we prove the existence not in BV, but in the nonreflexive space W1,1 0 (Ω).