An upper bound for positive solutions of the equation Δ𝑢=𝑢^{𝛼}
Electronic research announcements of the American Mathematical Society, Tome 10 (2004), pp. 103-112
Cet article a éte moissonné depuis la source American Mathematical Society
In 2002 Mselati proved that every positive solution of the equation $\Delta u=u^2$ in a bounded domain of class $C^4$ is the limit of an increasing sequence of moderate solutions. (A solution is called moderate if it is dominated by a harmonic function.) As a part of his proof, he established an upper bound (in terms of the capacity of $K$) for solutions vanishing off a compact subset $K$ of $\partial E$. We use a different kind of capacity (we call it the Poisson capacity) and we establish in terms of this capacity an upper bound for solutions of $\Delta u=u^\alpha$ with $1\alpha \le 2$. This is a part of the program: to classify all positive solutions of this equation.
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author = {Kuznetsov, S.},
title = {An upper bound for positive solutions of the equation {\ensuremath{\Delta}\ensuremath{\mathit{u}}=\ensuremath{\mathit{u}}^{𝛼}}},
journal = {Electronic research announcements of the American Mathematical Society},
pages = {103--112},
year = {2004},
volume = {10},
doi = {10.1090/S1079-6762-04-00135-0},
url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-04-00135-0/}
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Kuznetsov, S. An upper bound for positive solutions of the equation Δ𝑢=𝑢^{𝛼}. Electronic research announcements of the American Mathematical Society, Tome 10 (2004), pp. 103-112. doi: 10.1090/S1079-6762-04-00135-0
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