In the regular but not strongly regular boundary conditions, periodic and antiperiodic boundary conditions are the ones more commonly studied.
This paper presents a new fictitious domain formulation for the solution of a strongly elliptic boundary value problem with Neumann boundary conditions for a bounded domain in a finite-dimensional Euclidean space with a smooth (possibly only Lipschitz) boundary.
On the strongly degenerate boundary, they formulated a new approach to prescribe the boundary value condition rather than define the Fichera function as treating the linear case.
The alterations seen in the geometric change fit predictions from models of place cell function in which place cells are driven strongly by boundary inputs and re-scale fields in response deformation of boundaries (Hartley et al. 2000).
The basis properties of other some operators with regular but not strongly regular boundary conditions are studied in [20 23].
Since ∥ r x ∥ ≠ 0 on ⋃ k ∂ C Ω k, strongly compatible boundary conditions on Ω will be strongly compatible on Ω ε for 0 < ε sufficiently small.
In the case when an operator is associated with the regular but not strongly regular boundary conditions, the root functions generally do not form even a usual basis.
Namely, such regions should not only have a strongly nonlinear boundary but also tend to be separated although they will not be far from each other.
The extracted thermal conductivities of the nanoporous Bi thin films are greatly suppressed, relative to those of bulk materials because of the strongly enhanced boundary scattering via charge carriers and bipolar diffusion at the pore surfaces [18].
Due to the impact of collision between the Indian Plate and the Eurasian Plate, the Liupanshan Thrust-Fold Belt (namely the Liupan Mountain in Fig. 2) was developed along the southwestern margin of the Ordos Basin, which resulted in the transformation of the west-southwestern margin into a strongly compressive boundary during the Cenozoic era (Yuan et al. 2007; Li and Li 2008).
This value is four times lower than that of the homologous bulk material (approximately 11 W/m∙K at 280 K), owing to the strongly enhanced boundary scattering via phonons, charge carriers, and bipolar diffusion induced by the nanoscale crystal grains and the thickness reduction [18, 21], which in turn results in a greatly reduced thermal conductivity of the Bi thin films.
