4 citations
4 papers
Sobolev solution for semilinear PDE with obstacle under monotonicity condition
A. Matoussi, M. Xu
We prove the existence and uniqueness of the solution of a semilinear PDE's and also PDE's with obstacle under monotonicity condition. Moreover we give the probabilistic interpreta…
Effective macroscopic dynamics of stochastic partial differential equations in perforated domains
Wei Wang, Daomin Cao, Jinqiao Duan
An effective macroscopic model for a stochastic microscopic system is derived. The original microscopic system is modeled by a stochastic partial differential equation defined on a…
Robin functions and distortion theorems for regular mappings
Vladimir N. Dubinin, Matti Vuorinen
Capacities of generalized condensers are applied to prove a two-point distortion theorem for conformal mappings. The result is expressed in terms of the Robin function and the Robi…
On conformal moduli of polygonal quadrilaterals
V. N. Dubinin, M. Vuorinen
The change of conformal moduli of polygonal quadrilaterals under some geometric transformations is studied. We consider the motion of one vertex when the other vertices remain fixe…