On the regularizing effect of strongly increasing lower order terms

Lucio Boccardo ()
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Lucio Boccardo: Università di Roma I, Dipartimento di Matematica

A chapter in Nonlinear Evolution Equations and Related Topics, 2003, pp 225-236 from Springer

Abstract: Abstract We show an existence result of bounded weak solutions for some semilinear Dirichlet problems, even if the right hand side belongs only to L1(Ω). The model example is $$ \left\{ \begin{gathered} - \Delta u + h(u) = f(x) in \Omega , \hfill \\ u = 0 on \partial \Omega , \hfill \\ \end{gathered} \right. $$ where Ω is a bounded open set in ℝ N , h(s) is a continuous and increasing function such that $$ \mathop{{\lim }}\limits_{{s \to \sigma }} h(s) = + \infty $$ , for some δ>0 We also show a nonexistence result for some measures as data as in the model example $$ \left\{ \begin{gathered} - \Delta u + h(u) = {\delta _{{x0}}} in \Omega , \hfill \\ u = 0 on \partial \Omega , \hfill \\ \end{gathered} \right. $$ where $$ {\delta _{{{x_{0}}}}} $$ is the Dirac mass in x 0(x 0∈Ω).

Keywords: Regularizing effect; singular data (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-7924-8_12

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DOI: 10.1007/978-3-0348-7924-8_12

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