Repositorio DSpace :: Examinando por Autor "Boccardo, Lucio"

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W01,1 -solutions for elliptic problems having gradient quadratic lower order terms
(Springer Nature, 2013-04-10) David, Arcoya; Boccardo, Lucio; Leonori, Tommaso; https://orcid.org/0000-0002-7284-2413; https://orcid.org/0000-0002-8067-0121; https://orcid.org/0000-0002-0848-4463
In this paper we deal with solutions of problems of the type (Formula presented). where 0 < α ≤ a(x) ≤ β, {pipe}b(x){pipe} ≤ γ, γ > 0, f ∈ L2 (Ω) and Ω is a bounded subset of ℝN with N ≥ 3. We prove the existence of at least one solution for such a problem in the space W01,1 (Ω) ∩ L2 (Ω) if the size of the lower order term satisfies a smallness condition when compared with the principal part of the operator. This kind of problems naturally appears when one looks for positive minima of a functional whose model is: (Formula presented). where in this case a(x) ≡ b(x) = α > 0.