Uniqueness of solutions for some degenerate nonlinear elliptic equations
Volume 41 / 2014
Applicationes Mathematicae 41 (2014), 93-106
MSC: 35J70, 35J60.
DOI: 10.4064/am41-1-8
Abstract
We investigate the existence and uniqueness of solutions to the Dirichlet problem for a degenerate nonlinear elliptic equation $$ - \sum _{i,j=1}^nD_j(a_{ij}(x)D_iu(x)) + b(x)u(x) + \mathop {\rm div}\nolimits (\varPhi (u(x))) = g(x) - \sum _{j=1}^n f_j(x) \ \text {on} \ \varOmega $$ in the setting of the space $H_0(\varOmega )$.
