In this paper we deal with a nonlinear elliptic problem, whose model is $$ \left\{ \begin{array}{cc} \disp - \Delta u = B \frac{|D u |^2}{ u} +f & \mbox{in $\Omega$,} \\[1.5 ex] \disp u=0 & \mbox{on $\partial\Omega$}, \end{array} \right. $$ where $B>0$ and $f\geq0$ belongs to a Lebesgue space. We prove the existence of positive solutions in suitable Sobolev spaces (depending on $f$ and $B$).

Arcoya, D., Boccardo, L., Leonori, T., Porretta, A. (2010). Some elliptic problems with singular natural growth lower order terms. JOURNAL OF DIFFERENTIAL EQUATIONS, 249(11), 2771-2795 [10.1016/j.jde.2010.05.009 |].

Some elliptic problems with singular natural growth lower order terms

PORRETTA, ALESSIO
2010-01-01

Abstract

In this paper we deal with a nonlinear elliptic problem, whose model is $$ \left\{ \begin{array}{cc} \disp - \Delta u = B \frac{|D u |^2}{ u} +f & \mbox{in $\Omega$,} \\[1.5 ex] \disp u=0 & \mbox{on $\partial\Omega$}, \end{array} \right. $$ where $B>0$ and $f\geq0$ belongs to a Lebesgue space. We prove the existence of positive solutions in suitable Sobolev spaces (depending on $f$ and $B$).
2010
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
English
Nonlinear elliptic equations, singular natural growth gradient terms, boundary condition.
Arcoya, D., Boccardo, L., Leonori, T., Porretta, A. (2010). Some elliptic problems with singular natural growth lower order terms. JOURNAL OF DIFFERENTIAL EQUATIONS, 249(11), 2771-2795 [10.1016/j.jde.2010.05.009 |].
Arcoya, D; Boccardo, L; Leonori, T; Porretta, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/11965
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