We prove existence, regularity and nonexistence results for problems whose model is -Lambda u = f(x)/u gamma in Omega, with zero Dirichlet conditions on the boundary of an open, bounded subset Omega of R(N). Here gamma > 0 and f is a nonnegative function on Omega. Our results will depend on the summability of f in some Lebesgue spaces, and on the values of gamma (which can be equal, larger or smaller than 1).
Semilinear elliptic equations with singular nonlinearities / Boccardo, Lucio; Orsina, Luigi. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 37:3-4(2010), pp. 363-380. [10.1007/s00526-009-0266-x]
Semilinear elliptic equations with singular nonlinearities
BOCCARDO, Lucio;ORSINA, Luigi
2010
Abstract
We prove existence, regularity and nonexistence results for problems whose model is -Lambda u = f(x)/u gamma in Omega, with zero Dirichlet conditions on the boundary of an open, bounded subset Omega of R(N). Here gamma > 0 and f is a nonnegative function on Omega. Our results will depend on the summability of f in some Lebesgue spaces, and on the values of gamma (which can be equal, larger or smaller than 1).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
