论文标题
P-Laplacian在薄通道中具有局部周期性粗糙边界
The p-Laplacian in thin channels with locally periodic rough boundaries
论文作者
论文摘要
在这项工作中，我们分析了$ p $ laplacian方程的解决方案的渐近行为 $$ r^\ varepsilon = \ left \ lbrace（x，y）\ in \ mathbb {r}^2：x \ in（0,1）\ mbox {and} 0 <y <y <\ varepsilon g \ left（x}}}/{x}/{x}/{x \ varepsilon} 我们采用平滑函数$ g：（0,1）\ times \ mathbb {r} \ mapsto \ mathbb {r} $，$ l $ - periodic在第二个变量中，这使我们可以考虑在上边界处的本地定期振荡。由于正参数$ \ varepsilon $为零，因此建立了薄域的情况将解决方案的限制传递到限制。
In this work we analyze the asymptotic behavior of the solutions of the $p$-Laplacian equation with homogeneous Neumann boundary conditions set in bounded thin domains as $$R^\varepsilon=\left\lbrace(x,y)\in\mathbb{R}^2:x\in(0,1)\mbox{ and }0<y<\varepsilon G\left(x,{x}/{\varepsilon}\right)\right\rbrace.$$ We take a smooth function $G:(0,1)\times\mathbb{R} \mapsto \mathbb{R}$, $L$-periodic in the second variable, which allows us to consider locally periodic oscillations at the upper boundary. The thin domain situation is established passing to the limit in the solutions as the positive parameter $\varepsilon$ goes to zero.
