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Existence and regularity results for some singular elliptic problems
No full textWe are interested in the study of existence, uniqueness and regularity of solutions for nonlinear elliptic problems whose model is the linear boundary value problem [GRAPHICS] where 0 is an element of ohm. We will prove that such results strongly depend on the size of the lower order term, that is on the constant B
Asymptotic behavior of solutions for parabolic equations with natural growth term and irregular data
No full textLarge solutions to quasilinear problems involving the p-Laplacian as p diverges
No full textIn this paper we deal with large solutions to
{−Δ+|∇|=()=+∞ in Ω, on ∂Ω,
where Ω⊂R , with ≥1, is a smooth, open, connected, and bounded domain, ≥2, >0, −1<≤ and ∈(Ω)∩∞(Ω). We are interested in studying their behavior as p diverges. Our main result states that, if, in some sense, the domain Ω is large enough, such solutions converge locally uniformly to a limit function that turns out to be a large solution of a suitable limit equation (that involves the ∞-Laplacian). Otherwise, if Ω is small, we have a complete blow-up
Local Properties of Solutions of Elliptic Equations Depending on Local Properties of the Data
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Ground states of self-gravitating elastic bodies
No full textThe existence of static, self-gravitating elastic bodies in the non-linear theory of elasticity is established. Equilibrium configurations of self-gravitating elastic bodies close to the reference configuration have been constructed in Beig and Schmidt (Proc R Soc Lond, 109-115, 2003) using the implicit function theorem. In contrast, the steady states considered in this article correspond to deformations of the relaxed state with no size restriction and are obtained as minimizers of the energy functional of the elastic body
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