On some Bernoulli free boundary type problems for general elliptic operators
Published online by Cambridge University Press: 18 September 2007
Abstract
We consider some Bernoulli free boundary type problems for a general class of quasilinear elliptic (pseudomonotone) operators involving measures depending on unknown solutions. We treat those problems by applying the Ambrosetti–Rabinowitz minimax theorem to a sequence of approximate nonsingular problems and passing to the limit by some a priori estimates. We show, by means of some capacity results, that sometimes the measures are regular. Finally, we give some qualitative properties of the solutions and, for a special case, we construct a continuum of solutions.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 5 , October 2007 , pp. 895 - 911
- Copyright
- 2007 Royal Society of Edinburgh
- 5
- Cited by