Linear and nonlinear degenerate abstract parabolic equations with variable coefficients are studied. Here the equation and boundary conditions are degenerated on all boundary and contain someâ€¦ (More)

In this note we prove a sufficient condition for commutators of fractional integral operators to belong to Vanishing Morrey spaces V L p,Î». In doing this we use an extension on Morrey spaces of anâ€¦ (More)

In this note we prove local L p-regularity for the highest-order derivatives of an el-liptic system of arbitrary order in nondivergence form where the coefficients of the principal part are taken inâ€¦ (More)

In this note, we consider the regularity problem under the critical condition to the Boussinesq equations with zero heat conductivity. The Serrin type regularity criteria are established in terms ofâ€¦ (More)

This article presents a study of the regular oblique derivative problem n âˆ‘ i,j=1 a(x) âˆ‚2u âˆ‚xiâˆ‚xj = f(x) âˆ‚u âˆ‚`(x) + Ïƒ(x)u = Ï†(x) . Assuming that the coefficients aij belong to the Sarasonâ€™s class ofâ€¦ (More)

We prove a Harnack inequality for the positive solutions of a SchrÃ¶dinger type equation L0 u + V u = 0, where L0 is an operator satisfying the HÃ¶rmander's condition and V belongs to a class ofâ€¦ (More)

In this paper, new classes of functions are defined. These spaces generalize Lorentz spaces and give a refinement of Lebesgue spaces, weak-Lebesgue spaces, and Morrey spaces. Some embeddings betweenâ€¦ (More)

In this article, we establish the existence of weak solutions for a nonlinear transmission problem involving nonlocal coefficients of p(x)-Kirchhoff type in two different domains, which are connectedâ€¦ (More)