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On some Bernoulli free boundary type problems for general elliptic operators


Díaz Díaz, Jesús Ildefonso and Padial Molina, Juan Francisco and Rakotoson, Jean Michel Theresien (2007) On some Bernoulli free boundary type problems for general elliptic operators. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 137 (5). pp. 895-911. ISSN 0308-2105

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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.

Item Type:Article
Uncontrolled Keywords:t-set; equations; existence; confinement; stellarator; regularity; datum.
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:15288

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