Interior Estimates for Singularly Perturbed Problems

  • Dietrich Göhde

    Leipzig, Germany


The solution of the Dirichlet problem for a singularly perturbed elliptic differential equation ϵL1u+L0u=h\epsilon L_1u + L_0u = h of order 2m2m converges, for ϵ0\epsilon \to 0, outside of the boundary layer uniformly to a solution of the degenerate elliptic equation L0w=hL_0w = h of lower order. It is shown in the case of order zero of L0L_0 this assertion may be proved immediately, i.e., without the usual construction of boundary layer terms, but rather elementary and on weak smoothness conditions with respect to the boundary of the domain.

Cite this article

Dietrich Göhde, Interior Estimates for Singularly Perturbed Problems. Z. Anal. Anwend. 3 (1984), no. 4, pp. 315–328

DOI 10.4171/ZAA/110