Elliptic equations with vertical asymptotes in the nonlinear term

@inproceedings{Dupaigne2006EllipticEW,
  title={Elliptic equations with vertical asymptotes in the nonlinear term},
  author={Louis Dupaigne and Augusto Ponce and Alessio Porretta},
  year={2006}
}
We study the existence of solutions of the nonlinear problem { −∆u + g(u) = μ in Ω, u = 0 on ∂Ω, (0.1) where μ is a bounded measure and g is a continuous nondecreasing function such that g(0) = 0. In this paper, we assume that the nonlinearity g satisfies lim t↑1 g(t) = +∞. (0.2) Problem (0.1) need not have a solution for every measure μ. We prove that, given μ, there exists a “closest” measure μ∗ for which (0.1) can be solved. We also explain how assumption (0.2) makes problem (0.1) different… CONTINUE READING

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