Free boundary problems for the laplace equation: A priori estimates, existence theorems, asymptotic behaviours

摘要

AbstractThis work is devoted to Free Boundary Problems with Laplace equation Δu=fin the domain and the two conditions on the Free Boundaryu= 1 and gradu = λ = const. In the model problems which we study, three cases arise: 1)f= 0, λ is given, 2)f= 0, λ is unknown and the length of the Free Boundary is given, 3)f≠ 0, λ = 0 (Obstacle Pr