Journal of the Korean Mathematical Society (대한수학회지)
- Volume 31 Issue 3
- /
- Pages.401-416
- /
- 1994
- /
- 0304-9914(pISSN)
- /
- 2234-3008(eISSN)
The intermediate solution of quasilinear elliptic boundary value problems
- Ko, Bong-Soo (Department of Mathematics Education Cheju National University)
- Published : 1994.08.01
Abstract
We study the existence of an intermediate solution of nonlinear elliptic boundary value problems (BVP) of the form $$ (BVP) {\Delta u = f(x,u,\Delta u), in \Omega {Bu(x) = \phi(x), on \partial\Omega, $$ where $\Omega$ is a smooth bounded domain in $R^n, n \geq 1, and \partial\Omega \in C^{2,\alpha}, (0 < \alpha < 1), \Delta$ is the Laplacian operator, $\nabla u = (D_1u, D_2u, \cdots, D_nu)$ denotes the gradient of u and $$ Bu(x) = p(x)u(x) + q(x)\frac{d\nu}{du} (x), $$ where $\frac{d\nu}{du} denotes the outward normal derivative of u on $\partial\Omega$.
Keywords