Abstract.
We study the equation −\(\Delta u + g(x, u) = \mu\), where g(·, s) is finite outside sets of zero H 1-capacity, \(\forall s \in {\mathbb{R}}\), and μ is a diffuse measure. As an application, we provide a positive answer to a question of Lucio Boccardo concerning existence of solutions of an elliptic system with absorption.
A Lucio
“Tu se’ lo mio maestro e ’l mio autore”
(Dante, Inferno, I, 85)
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Orsina, L., Ponce, A.C. Semilinear elliptic equations and systems with diffuse measures. J. evol. equ. 8, 781–812 (2008). https://doi.org/10.1007/s00028-008-0446-32
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DOI: https://doi.org/10.1007/s00028-008-0446-32