Mixed boundary value problems for parabolic equations in Sobolev spaces with mixed-norms

Parabolic Equations with Partially Vmo Coefficients and Boundary Value Problems in Sobolev Spaces with Mixed Norms

Second order parabolic equations in Sobolev spaces with mixed norms are studied. The leading coefficients (except a) are measurable in both time and one spatial variable, and VMO in the other spatial variables. The coefficient a is measurable in time and VMO in the spatial variables. The unique solvability of equations in the whole space is applied to solving Dirichlet and oblique derivative pr...

Parabolic Equations with Vmo Coefficients in Spaces with Mixed Norms

An Lq(Lp)-theory of divergence and non-divergence form parabolic equations is presented. The main coefficients are supposed to belong to the class V MOx, which, in particular, contains all measurable functions depending only on t. The method of proving simplifies the methods previously used in the case p = q.

Mixed Two-point Boundary-value Problems for Impulsive Differential Equations

In this article, we prove the existence of solutions to mixed twopoint boundary-value problem for impulsive differential equations by variational methods, in both resonant and the non resonant cases.

Initial - Boundary Value Problems for Parabolic Equations

Boundary value problems for mixed type equations and applications