scholarly journals Existence results for a nonlinear transmission problem

2015 ◽  
Vol 430 (2) ◽  
pp. 718-741 ◽  
Author(s):  
M. Dalla Riva ◽  
G. Mishuris
Keyword(s):  
Existence Results ◽  
Transmission Problem ◽  
Nonlinear Transmission

scholarly journals Existence results for a nonlinear nonautonomous transmission problem via domain perturbation

2021 ◽  
pp. 1-26
Author(s):  
Matteo Dalla Riva ◽  
Riccardo Molinarolo ◽  
Paolo Musolino
Keyword(s):  
Boundary Value Problem ◽  
Laplace Equation ◽  
Boundary Value ◽  
Perturbation Parameter ◽  
Existence Results ◽  
Transmission Problem ◽  
Perforated Domain ◽  
Analytic Dependence ◽  
Domain Perturbation ◽  
Fixed Domain

In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. The problem is defined in a pair of sets consisting of a perforated domain and an inclusion whose shape is determined by a suitable diffeomorphism $\phi$ . First we analyse the case in which the inclusion is a fixed domain. Then we will perturb the inclusion and study the arising boundary value problem and the dependence of a specific family of solutions upon the perturbation parameter $\phi$ .

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