We prove a priori bounds for weak solutions of semilinear elliptic equations of the form −Δu = cu^p, with 0 < p < p_s = (d + 2)/(d − 2), d ≥ 3, posed on a bounded domain Ω of Rd with boundary conditions u = 0. The bounds are quantitative and we give explicit expressions for all the involved constants. These estimates also allow to compare solutions corresponding to different values of p, an in particular take the limit p → 1. Besides their own interest, these results are useful in the study of the asymptotic convergence with rate of the solutions to the Cauchy-Dirichlet problem for the Fast Diffusion Equation.
Quantitative bounds for subcritical semilinear elliptic equations
GRILLO, GABRIELE;
2013-01-01
Abstract
We prove a priori bounds for weak solutions of semilinear elliptic equations of the form −Δu = cu^p, with 0 < p < p_s = (d + 2)/(d − 2), d ≥ 3, posed on a bounded domain Ω of Rd with boundary conditions u = 0. The bounds are quantitative and we give explicit expressions for all the involved constants. These estimates also allow to compare solutions corresponding to different values of p, an in particular take the limit p → 1. Besides their own interest, these results are useful in the study of the asymptotic convergence with rate of the solutions to the Cauchy-Dirichlet problem for the Fast Diffusion Equation.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
CM 2013.pdf
Accesso riservato
:
Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione
308.53 kB
Formato
Adobe PDF
|
308.53 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.