Coercive solvability of the nonlocal boundary value problem for parabolic differential equations

Abstract

The nonlocal boundary value problem, v′(t)+Av(t)=f(t)(0≤t≤1),v(0)=v(λ)+μ(0<λ≤1), in an arbitrary Banach space E with the strongly positive operator A, is considered. The coercive stability estimates in Hölder norms for the solution of this problem are proved. The exact Schauder's estimates in Hölder norms of solutions of the boundary value problem on the range {0≤t≤1,xℝ n} for 2m-order multidimensional parabolic equations are obtaine.