In this paper, we prove existence of weak solutions in W1,20 (Ω) ∩L∞ (Ω) for the gradient coupled Dirichlet system (equation presented). We also prove that if f (x), g(x) ≈ ¥ 0 (of course ≈ ¢ 0 a.e.), then u(x), (x) ≈ ¥ 0 and the sets {u = 0} and {φ = 0} have zero Lebesgue measure.
Existence of solutions for gradient coupled Dirichlet systems / Boccardo, L.; Orsina, L.. - In: ESAIM. COCV. - ISSN 1292-8119. - 30:(2024). [10.1051/cocv/2024011]
Existence of solutions for gradient coupled Dirichlet systems
Boccardo L.
;Orsina L.
2024
Abstract
In this paper, we prove existence of weak solutions in W1,20 (Ω) ∩L∞ (Ω) for the gradient coupled Dirichlet system (equation presented). We also prove that if f (x), g(x) ≈ ¥ 0 (of course ≈ ¢ 0 a.e.), then u(x), (x) ≈ ¥ 0 and the sets {u = 0} and {φ = 0} have zero Lebesgue measure.File allegati a questo prodotto
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