We establish existence and uniqueness of solution for the homogeneous Dirichlet problem associated to a fairly general class of elliptic equations modeled by $$ -\Delta u= h(u){f} \ \ \text{in}\,\ \Omega, $$ where $f$ is an irregular datum, possibly a measure, and $h$ is a continuous function that may blow up at zero. We also provide regularity results on both the solution and the lower order term depending on the regularity of the data, and we discuss their optimality.

Finite and Infinite energy solutions of singular elliptic problems: existence and uniqueness / Oliva, Francescantonio; Petitta, Francesco. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 264:1(2018), pp. 311-340. [10.1016/j.jde.2017.09.008]

Finite and Infinite energy solutions of singular elliptic problems: existence and uniqueness

OLIVA, FRANCESCANTONIO;PETITTA, FRANCESCO
2018

Abstract

We establish existence and uniqueness of solution for the homogeneous Dirichlet problem associated to a fairly general class of elliptic equations modeled by $$ -\Delta u= h(u){f} \ \ \text{in}\,\ \Omega, $$ where $f$ is an irregular datum, possibly a measure, and $h$ is a continuous function that may blow up at zero. We also provide regularity results on both the solution and the lower order term depending on the regularity of the data, and we discuss their optimality.
Nonlinear elliptic equations; Singular elliptic equations; Uniqueness; Measure data
01 Pubblicazione su rivista::01a Articolo in rivista
Finite and Infinite energy solutions of singular elliptic problems: existence and uniqueness / Oliva, Francescantonio; Petitta, Francesco. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 264:1(2018), pp. 311-340. [10.1016/j.jde.2017.09.008]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1005916
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