RT Journal Article
T1 Very rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a non uniformly Lipschitz deformation
A1 Arrieta Algarra, José María
A1 Bruschi, Simone M.
AB We continue the analysis started in [3] and announced in [2], studying the behavior of solutions of nonlinear elliptic equations  in  ε with nonlinear boundary conditions of type  , when the boundary of the domain varies very rapidly. We show that if the oscillations are very rapid, in the sense that, roughly speaking, its period is much smaller than its amplitude and the function  is of a dissipative type, that is, it satisfies  , then the boundary condition in the limit problem is  , that is, we obtain a homogeneus Dirichlet boundary condition. We show the convergence of solutions in  and  norms and the convergence of the eigenvalues and eigenfunctions of the linearizations around the solutions. Moreover, if a solution of the limit problem is hyperbolic (non degenerate) and some extra conditions in  are satisfied, then we show that there exists one and only one solution of the perturbed problem nearby.
PB American Institute of Mathematical Sciences
SN 1531-3492
YR 2010
FD 2010
LK https://hdl.handle.net/20.500.14352/41970
UL https://hdl.handle.net/20.500.14352/41970
LA eng
NO MICINN
NO DGES
NO FAPESP
NO Grupo 920894  BSCH-UCM
DS Docta Complutense
RD 6 abr 2025