A survey of results on nonlinear Venttsel problems

summary:We review the recent results for boundary value problems with boundary conditions given by second-order integral-differential operators. Particular attention has been paid to nonlinear problems (without integral terms in the boundary conditions) for elliptic and parabolic equations. For these problems we formulate some statements concerning a priori estimates and the existence theorems in Sobolev and Hölder spaces

Nonstationary Venttsel problems with discontinuous data

The paper deals with Venttsel boundary problems for second-order linear and quasilinear parabolic operators with discontinuousprincipal coefficients. These are supposed to be functions of vanishing mean oscillationwith respect to the space variables, while only measurabilityis required in the time-variable. We derive aprioriestimates in composite Sobolev spaces for the strong solutions, and develop maximal regularity and strong solvability theory for such problems