Venttsel’ problems in fractal domains

Fractional Equations Via Convergence of Forms

“…A similar example can be given for domains with fractal boundaries as in [22] where the authors have obtained asymptotic results for skew Brownian diffusions across Koch interfaces by using M −convergence results proved in [20], [24], [25]. We recall that M −convergence results have been obtained on fractal structures in order to study several boundary value problems ( [2], [23], [56], [57], [58]), reinforcement problems for variational inequalities ( [26]), dynamical quasi-filling fractal layers, layered fractal fibers and potentials ( [27], [74], [75]).…”

Nonlocal Venttsel' diffusion in fractal‐type domains: Regularity results and numerical approximation

“…Let f ∈ L 2 (Ω, m) and b and 2 (u) be as defined above. For every t ∈ [0, T] let u ∈ V 2 (Ω, K n ) be a solution of problem (8). Then there exists a positive constant C = C( ) such that…”

“…The literature on linear and quasi-linear Venttsel' problems in both regular and irregular domains is huge (see, eg, other studies [6][7][8][9][10] and the references listed in). In all these papers, it addressed the study of existence and uniqueness properties of the solution by a semigroup approach.…”

On two-dimensional nonlocal Venttsel' problems in piecewise smooth domains

“…Lately Venttsel' problems in irregular domains (for example having prefractal or fractal boundary) have been widely investigated, see e.g. [12] and [10] and the references listed in.…”