Boundary singularities of solutions of sublinear elliptic equations.
In this paper we consider general second order, symmetric and strongly elliptic parabolic systems with real valued and constant coefficients in the setting of a class of time-varying, non-smooth infinite cylindersΩ = {(x0,x,t) ∈ R x Rn-1 x R: x0 > A(x,t)}.We prove solvability of Dirichlet, Neumann as well as regularity type problems with data in Lp and Lp1,1/2 (the parabolic Sobolev space having tangential (spatial) gradients and half a time derivative in Lp) for p ∈ (2 − ε, 2 + ε) assuming...
We study the behaviour of weak solutions (as well as their gradients) of boundary value problems for quasi-linear elliptic divergence equations in domains extending to infinity along a cone.