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On a generalized Stokes problem

Václav Mácha (2011)

Open Mathematics

We deal with a generalization of the Stokes system. Instead of the Laplace operator, we consider a general elliptic operator and a pressure gradient with small perturbations. We investigate the existence and uniqueness of a solution as well its regularity properties. Two types of regularity are provided. Aside from the classical Hilbert regularity, we also prove the Hölder regularity for coefficients in VMO space.

On a phase-field model with a logarithmic nonlinearity

Alain Miranville (2012)

Applications of Mathematics

Our aim in this paper is to study the existence of solutions to a phase-field system based on the Maxwell-Cattaneo heat conduction law, with a logarithmic nonlinearity. In particular, we prove, in one and two space dimensions, the existence of a solution which is separated from the singularities of the nonlinear term.

On a semilinear elliptic equation in n

Gianni Mancini, Kunnath Sandeep (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We prove existence/nonexistence and uniqueness of positive entire solutions for some semilinear elliptic equations on the Hyperbolic space.

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