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| REGULARITY RESULTS FOR SOMEQUASI-LINEAR ELLIPTIC SYSTEMS INVOLVINGCRITICAL EXPONENTS |
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Citation： |
HU Yexin,LI Juan.REGULARITY RESULTS FOR SOMEQUASI-LINEAR ELLIPTIC SYSTEMS INVOLVINGCRITICAL EXPONENTS[J].Chinese Annals of Mathematics B,2005,26(1):119~126 |
| Page view： 1208
Net amount： 937 |
Authors： |
HU Yexin; LI Juan |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10271077). |
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| Abstract： |
The authors show the regularity of weak solutions for some typical
quasi-linear elliptic systems governed by two $p$-Laplacian
operators. The weak solutions of the following problem with lack
of compactness are proved to be regular when $a(x)$ and
$\alpha,\beta,p,q$ satisfy some conditions: $$\begin{cases}
-\Delta_{p} u+a(x) |u|^{\alpha-1}|v|^{\beta+1}u=|u|^{p^*-2}u,\qquad &x
\in \Omega,\\[1mm]
-\Delta _{q}v +a(x)|u|^{\alpha+1}|v|^{\beta-1}v=|v|^{q^*-2}v, &x\in
\Omega,\\[1mm]
u(x)=v(x)=0, &x\in \partial\Omega,
\end{cases}$$
where $\Omega\subset R^N$ $(N\geq 3)$
is a smooth bounded domain. |
Keywords： |
Elliptic equation system, p-Laplacian operator, Critical Sobolev exponent,
Regularity |
Classification： |
35J65 |
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