Semilinear elliptic equations with singular nonlinearities

By Lucio Boccardo, Luigi Orsina. 2010

349 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/afb2d971557107d07ecf384beec82a062f18e01b

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Mixed local and nonlocal Sobolev inequalities with extremal and associated quasilinear singular elliptic problems (2021, methodology): “Our contribution: We start with the existence results (Theorem 2.13-2.15) for the problem (S), where the idea stem from the approximation approach in Boccardo-Orsina [17].”
The effect of the Hardy potential in some Calder\'on-Zygmund properties for the fractional Laplacian (2015, background): “The local case (s = 1) with λ = 0 was studied in [13].”
Combined effects in mixed local–nonlocal stationary problems (2021, background): “γ ≫ 1 (see [38]) or f ∈ L(Ω) when r is close to 1 (see [16]), we cannot always expect our solution u in H(1) 0 (Ω) and in place of that, either we have u α ∈ H(1) 0 (Ω) for some α ≥ 1 or u ∈ W 1,q 0 (Ω) for some q ∈ [1, 2).”
On singular elliptic equations with measure sources (2015, methodology): “9) It was proved in [8] the existence of a weak solution vn of (2.”
Finite and infinite energy solutions of singular elliptic problems: Existence and uniqueness (2016, background): “1) is proven (at least in the sense of approxima ting sequences) in [6] if the measure is too concentrated, while in [39] sharp existence results are obt ained in the measure is diffuse enough; here concentration and diffusion is intended in the sense of capa city.”
Existence and uniqueness for p-Laplace equations involving singular nonlinearities (2016, methodology): “In [4] the semilinear case p = 2 is considered but the adaptation of the technique to the quasilinear case is not difficult.”
Nonlocal problems with singular nonlinearity (2016, methodology): “m 1.2 will be carried out considering ﬁrst the simplest case 0 <γ≤ 1 (see Theorem 3.2) and then the case γ > 1 (see Theorem 3.6). The proof relies on the well established technique introduce in [3]. Actually, via Shauder ﬁxed point theorem, we ﬁnd a solution to a regularized problem and then w”