Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

For boundary value problems for degenerate-elliptic equations of second order in ⊂ Rn there are cases when a closed surface exists, dividing into two subdomains in such a manner that two new correct boundary value problems can be formulated without introducing new boundary conditions. Such surfaces are called interior boundaries. Some theoretical results regarding the connections between the solutions of the original problem and the two new problems are given. Some numerical experiments using the finite elements method are carried out trying to visualize the effects of the presence of such interior boundary when n = 2. Also some more precise study of the solutions in the case n = 2 is presented.