Bounded weak solutions of an elliptic-parabolic Neumann problem

Entropy Solutions for Nonlinear Elliptic Anisotropic Homogeneous Neumann Problem

Remarks on weak solutions for a nonlocal parabolic problem

where Ω is a smooth bounded open subset of RN with regular boundary Γ. In problem (1.1) a and f are both continuous functions, whose properties will be introduced when necessary, l : L2(Ω) → R is a nonlinear form, h ∈ L2(0,T ;H−1(Ω)), and T > 0 is some fixed time. System (1.1) is studied, for instance, in papers of Chipot and Lovat [4] in case f = f (x) depends only on the variable x. In this w...

NEUMANN PROBLEM FOR NON-DIVERGENCE ELLIPTIC AND PARABOLIC EQUATIONS WITH BMOx COEFFICIENTS IN WEIGHTED SOBOLEV SPACES

We prove the unique solvability in weighted Sobolev spaces of non-divergence form elliptic and parabolic equations on a half space with the homogeneous Neumann boundary condition. All the leading coefficients are assumed to be only measurable in the time variable and have small mean oscillations in the spatial variables. Our results can be applied to Neumann boundary value problems for stochast...

Asymptotic analysis of an elliptic-parabolic moving boundary problem

AMS Subject Classiication. We gratefully acknowledge the support of the Dutch Organisation for Scientiic Research (NWO) and the British Council.

Stability of equilibria in an elliptic-parabolic moving boundary problem

We discuss a moving boundary problem modeling tumor growth in in vitro tissue cultures. It is shown that the unique flat steady state solution is exponentially stable with respect to general (sufficiently smooth) perturbations. Furthermore, it is also shown that any solution to the problem becomes instantaneously real analytic in space and in time.