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

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 $B$).
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - Analisi Matematica
eng
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
Articolo su rivista
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/11965
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact