We establish \(L_{q,p}\)-estimates and solvability for mixed Dirichlet–conormal problems parabolic equations in a cylindrical Reifenberg-flat domain with rough time-dependent separation.

Presented in this paper is an analytic approximation to the thermal-fluid problem involving mixed and forced convective heat transfer from a rotating isothermal cylinder placed in a non-uniform stream shear-flow. The approximation is obtained using a series expansion of the scaled boundary layer equations in terms of a boundary layer variable which is directly proportional to the time variable ...

We study extrema of the first and the second mixed eigenvalues of the Laplacian on the disk among some families of Dirichlet–Neumann boundary conditions. We show that the minimizer of the second eigenvalue among all mixed boundary conditions lies in a compact 1–parameter family for which an explicit description is given. Moreover, we prove that among all partitions of the boundary with bounded ...

Presented in this paper is an analytic approximation to the thermal-fluid problem involving mixed convective heat transfer from a rotating isothermal cylinder placed in a non-uniform stream shear flow. The approximation is obtained using a series expansion of the scaled boundary layer equations in terms of an appropriate boundary layer variable. The resulting approximation is valid both for sma...

Motivated by the paraxial narrow–angle approximation of the Helmholtz equation in domains of variable topography that appears as an important application in Underwater Acoustics, we analyze a general Schrödinger-type equation posed on two-dimensional variable domains with mixed boundary conditions. The resulting initialand boundary-value problem is transformed into an equivalent one posed on a ...

We study the boundary regularity of solutions of the mixed problem for Laplace’s equation in a Lipschitz graph domain Ω whose boundary is decomposed as ∂Ω = N ∪ D, where N ∩ D = ∅. For a subclass of these domains, we show that if the Neumann data g is in Lp(N) and if the Dirichlet data f is in the Sobolev space L(D), for 1 < p < 2, then the mixed boundary problem has a unique solution u for whi...

Abstract We study the first eigenvalue of the Laplace equation in a bounded domain in R (d = 2, 3) with mixed Neumann–Dirichlet (Zaremba) boundary conditions. The Neumann condition is imposed on most of the boundary and the Dirichlet boundary consists of a cluster of small windows. When the windows are well separated the first eigenvalue is asymptotically the sum of eigenvalues of mixed problem...

Mixed ionic-electronic conductors are widely used in devices for energy conversion and storage. Grain boundaries in these materials have nanoscale spatial dimensions, which can generate substantial resistance to ionic transport due to dopant segregation. Here, we report the concept of targeted phase formation in a Ce0.8Gd0.2O2-δ-CoFe2O4 composite that serves to enhance the grain boundary ionic ...

It is proved that the first eigenfunction of the mixed boundary-value problem for the Laplacian in a thin domain Ωh is localized either at the whole lateral surface Γh of the domain, or at a point of Γh, while the eigenfunction decays exponentially inside Ωh. Other effects, attributed to the high-frequency range of the spectrum, are discussed for eigenfunctions of the mixed boundary-value and N...