An initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary order elliptic differential operator is considered. Uniqueness and existence of the classical solution posed are proved by Fourier method. Sufficient conditions initial function right-hand side indicated, under which corresponding series converge absolutely uniformly. In case on $$N$$ -dimensional to...

The main objective of the paper is to state newly fixed point theorems for set-valued mappings in the framework of 0-complete partial metric spaces which speak about a location of a fixed point with respect to an initial value of the set-valued mapping by using some $C$-class functions. The results proved herein generalize, modify and unify some recent results of the existing literature. As an ...

We consider shape optimization problems, where the state is governed by elliptic partial differential equations (PDE). Using a regularization technique, unknown shapes are encoded via shape functions, turning the shape optimization into optimal control problems for the unknown functions. The method is studied for elliptic PDE to be solved in an unknown region (to be optimized), where the regula...

We consider the discretization of an optimal boundary control problem with distributed observation by the boundary concentrated finite element method. With an H(Ω) regular elliptic PDE on two-dimensional domains as constraint, we prove that the discretization error ‖u∗ − uh‖L2(Γ) decreases like N −δ, where N denotes the total number of unknowns. For the case δ = 1 in convex polygonal domains, t...

In these notes we present the pseudodifferential approach to elliptic boundary value problems for the Laplace operator acting on functions on a smoothly bounded compact domain in a compact manifold. This is an elaboration of the classical method of multiple layer potentials. After a short discussion of this method we consider the theory of homogeneous distributions on R. This is useful in our s...