Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains

Comments on behaviour of solutions of elliptic quasi-linear problems in a neighbourhood of boundary singularities

“…The estimate (20) we derive analogously to (6.1.7) [12] in virtue of Theorem 3.2 [3] and above proved Theorem 3.6 and the inequality .H W /.…”

On a Transmission Problem Related to Models of Electrocardiology

“…Since matrices M i and M e are positively defined and not degenerate, the problems (2), (3) can be studied in the framework of the theory of boundary (maybe ill-posed) problems for elliptic formally self-adjoint equations, see [1,2,5]. Moreover, notice that the problems above may be regarded as transmission problems for elliptic equations with discontinuous coefficients describing solutions in different domains of a continuum with the help of additional conditions on separating surfaces, see, for example, [6,7].…”

Long‐time asymptotics for a coupled thermoelastic plate–membrane system

“…The coefficient m ≥ 0 describes the damping (or the absence of damping) for the wave equation (3), whereas 𝜌 in (1) describes a structural damping on the plate. We will also include the situation when thermal effects for the plate are not taken into account by setting 𝜇 = 0 in (1) and omitting (2). We will assume that the plate is clamped at the exterior boundary Γ, namely,…”