Differential and Integral Equations

Higher order boundary estimates for blow-up solutions of elliptic equations

Claudia Anedda and Giovanni Porru

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Abstract

We investigate blow-up solutions of the equation $\Delta u=u^p+g(u)$ in a bounded smooth domain $\Omega$. If $p>1$ and if $g$ satisfies appropriate growth conditions (compared with the growth of $t^p$) as $t$ goes to infinity we find optimal asymptotic estimates of the solution $u(x)$ in terms of the distance of $x$ from the boundary $\partial\Omega$.

Article information

Source
Differential Integral Equations, Volume 19, Number 3 (2006), 345-360.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050517

Mathematical Reviews number (MathSciNet)
MR2215562

Zentralblatt MATH identifier
1212.35085

Subjects
Primary: 35J25
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35B40: Asymptotic behavior of solutions

Citation

Anedda, Claudia; Porru, Giovanni. Higher order boundary estimates for blow-up solutions of elliptic equations. Differential Integral Equations 19 (2006), no. 3, 345--360. https://projecteuclid.org/euclid.die/1356050517


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