‎in this work we prove malliavin differentiability for the solution to an sde with locally lipschitz and semi-monotone drift‎. ‎to prove this formula‎, ‎we construct a sequence of sdes with globally lipschitz drifts and show that the $p$-moments of their malliavin derivatives are uniformly bounded‎.

The aim of this work is to prove the global-in-time existence weak solutions for a viscoelastic phase separation model in three space dimensions. To end, we apply relative energy concept provided by [7]. We consider case regular polynomial-type potentials and positive mobilities, as well degenerate with logarithmic potential vanishing mobility.

These Lecture Notes are devoted to some aspects of the theory of the Navier-Stokes-Fourier system. We shall discuss 1) existence of weak solutions, 2) existence of suitable weak solutions and relative entropies, 3) weak strong uniqueness property in the class of weak solutions. For physical reasons, we shall limit ourselves to the three dimensional physical space, and for the sake of simplicity...

In this paper, a weak formulation of the discontinuous variable co-eecient Poisson equation with interfacial jumps is introduced. The existence, uniqueness and regularity of solutions of the Poisson equation are obtained. Finite diierence methods can be derived from the weak formulation. An abstract framework is given for proving convergence of the nite diierence methods for such problems. The ...

Existence and multiplicity of weak solutions for an elliptic system is studied. By using Ekeland’s variational principle and the mountain pass theorem, we prove existence of at least three weak solutions. AMS Subject Classifications: 35J40, 35J67.

In this article, we consider three types of solutions in Orlicz spaces for the quasilinear elliptic problem − div(a(|∇u|)∇u) = 0. By applying a comparison principle, we establish the relationships between viscosity supersolutions, weak supersolutions, and superharmonic functions.

Abstract. The compactness of weak solutions to the magnetohydrodynamic equations for the viscous, compressible, heat conducting fluids is considered in both the three-dimensional space R and the three-dimensional periodic domains. The viscosities, the heat conductivity as well as the magnetic coefficient are allowed to depend on the density, and may vanish on the vacuum. This paper provides a d...