Generalized multiplying boundary conditions and B-bounded semigroups

B-bounded Semigroups and C-existence Families

The aim of this paper is to investigate links of the recently introduced B-bounded semigroups [5] with other generalizations of semigroups, like C -regularized semigroups and C -existence families.

B-bounded semigroups and implicit evolution equations

where K : Z → X, L : Z → X, Z,X are, say, Banach spaces, and K,L are linear operators. There is a number of approaches to solving such problems; for example, [11, 12], similar in spirit the results of [15, 16, 17, 18] where an interesting notion of empathy is introduced, or [20] where a suitable change of space method is used. In this paper, we aim neither at a comprehensive treatment of the pr...

Absorption semigroups and dirichlet boundary conditions

Generalized bounded boundary turning functions

For a Jordan domain with smooth boundary, the boundary rotation h is defined as the total variation of the direction angle of the tangent to the boundary curve under a complete circuit. The domain is said to have bounded turning or rotation if h < 1 and the functions under such mappings are called functions of bounded boundary turning or rotation. We define a generalization of this concept and ...

On Generalized Ventcel's Type Boundary Conditions for Laplace Operator in a Bounded Domain

Ventcel boundary conditions are second order differential conditions that appear in asymptotic models. Like Robin boundary conditions, they lead to wellposed variational problems under a sign condition of a coefficient. Nevertheless situations where this condition is violated appeared in several works. The wellposedness of such problems was still open. This manuscript establishes, in the generi...