Affiliation:
1. Aix Marseille Université, CNRS, Centrale Marseille, I2M, 39 rue F. Joliot Curie, 13453, Marseille, France
Abstract
Abstract
We establish uniform a-priori bounds for solutions of the quasilinear problems
$$\begin{array}{}
\displaystyle
\begin{cases}
-{\it\Delta}_Nu=f(u)\quad&\mbox{in }{\it\Omega},\\
u=0\quad&\mbox{on }{\partial{\it\Omega}},
\end{cases}
\end{array}$$
where Ω ⊂ ℝN is a bounded smooth convex domain and f is positive, superlinear and subcritical in the sense of the Trudinger-Moser inequality. The typical growth of f is thus exponential. Finally, a generalisation of the result for nonhomogeneous nonlinearities is given. Using a blow-up approach, this paper completes the results in [1, 2], extending the class of nonlinearities for which the uniform a-priori bound applies.
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3 articles.
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