On the solvability of a class of a quasilinear elliptic partial differential equation - Beltran, Ryan James; Cabarrubias, Bituin; Roque, Marian (2017)
This paper considers a quasilinear elliptic problem posed on a two-component composite with a Dirichlet condition on the outer boundary and a jump condition of the solution on the interface. We establish the existence and uniqueness of a weak solution in some appropriate Sobolev space. We apply Schauder's fixed point theorem to prove the existence of the solution and impose some Lipschitz type conditions on the quasilinear term to show the uniqueness result. This work also exhibits an a priori estimate satisfied by the solution. (Author's abstract)
Includes bibliographical references (pages 142-143)
Keywords: Mathematics; Quasilinear elliptic problem; Stationary diffusion equation; Schauder\'s fixed point theorem; Two-component composite