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Article Dans Une Revue Communications in Partial Differential Equations Année : 2011

Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations

Résumé

We investigate stable solutions of elliptic equations of the type \begin{equation*} \left \{ \begin{aligned} (-\Delta)^s u&=\lambda f(u) \qquad {\mbox{ in $B_1 \subset \R^{n}$}} \\ u&= 0 \qquad{\mbox{ on $\partial B_1$,}}\end{aligned}\right . \end{equation*} where $n\ge2$, $s \in (0,1)$, $\lambda \geq 0$ and $f$ is any smooth positive superlinear function. The operator $(-\Delta)^s$ stands for the fractional Laplacian, a pseudo-differential operator of order $2s$. According to the value of $\lambda$, we study the existence and regularity of weak solutions $u$.

Dates et versions

hal-01338485 , version 1 (28-06-2016)

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Citer

Antonio Capella, Juan Dávila, Louis Dupaigne, Yannick Sire. Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations. Communications in Partial Differential Equations, 2011, 36 (8), pp.1353--1384. ⟨10.1080/03605302.2011.562954⟩. ⟨hal-01338485⟩
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