相关论文: Boundary Layer Solutions of Charge Conserving Pois…
In this paper, we investigate the boundary H\"{o}lder regularity for elliptic equations (precisely, the Poisson equation, linear equations in divergence form and non-divergence form, the p-Laplace equations and fully nonlinear elliptic…
We discuss the bound states of the massive Thirring model. Here, the periodic boundary condition equations for the Bethe ansatz solutions are numerically solved. It is found that the massive Thirring model has only one bound state and the…
When ions are crowded, the effect of steric repulsion between ions (which can produce oscillations in charge density profiles) becomes significant and the conventional Poisson-Boltzmann (PB) equation should be modified. Several modified PB…
This paper considers to the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. The diffraction problem formulated as boundary value problem for Helmholtz…
We use the Bethe Ansatz solution for the one dimensional Hubbard model with open boundary conditions and applied boundary fields to study the spectrum of bound states at the boundary. Depending on the strength of the boundary potentials one…
In this paper we are concerned with convergence of solutions of the Poisson equation with Neumann boundary conditions in a two-dimensional thin domain exhibiting highly oscillatory behavior in part of its boundary. We deal with the resonant…
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory but replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single…
Boundary integral equations are an efficient and accurate tool for the numerical solution of elliptic boundary value problems. The solution is expressed as a layer potential; however, the error in its evaluation grows large near the…
Macromolecules, when immersed in a polar solvent like water, become charged by a fixed surface charge density which is compensated by ``counter-ions'' moving out of the surface. Such classical particle systems exhibit poor screening…
In this paper we present in concise form recent results, with illustrative proofs, on solvability of the $L^p$ Dirichlet, Regularity and Neumann problems for scalar elliptic equations on Lipschitz domains with coefficients satisfying a…
We study equilibrium statistical mechanics of classical point counter-ions, formulated on 2D Euclidean space with logarithmic Coulomb interactions (infinite number of particles) or on the cylinder surface (finite particle numbers), in the…
We study the existence of a solution to the mixed boundary value problem for Helmholtz and Poisson type equations in a bounded Lipschitz domain $\Omega\subset\mathbb{R}^N$ and in $\mathbb{R}^N\setminus\Omega$ for $N\geq3$. The boundary…
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
We study a nonlinear boundary value problem driven by the $p$-Laplacian plus an indefinite potential with Robin boundary condition. The reaction term is a Carath\'eodory function which is asymptotically resonant at $\pm\infty$ with respect…
We consider a boundary value problem for the conductivity equation in a bounded domain containing an inclusion which is nearly touching to the domain's boundary. We assume that the domain and the inclusion are disks with conductivity jump…
Coupled double well (phi4) one-dimensional potentials abound in both condensed matter physics and field theory. Here we provide an exhaustive set of exact periodic solutions of a coupled $\phi^4$ model in an external field in terms of…
Scattering states with LEED asymptotics are calculated for a general non-muffin tin potential, as e.g. for a pseudopotential with a suitable barrier and image potential part. The latter applies especially to the case of low lying conduction…
We prove the solvability in Sobolev spaces $W^{1,2}_p$, $p>d+1$, of the terminal-boundary value problem for a class of fully nonlinear parabolic equations, including parabolic Bellman's equations, in bounded cylindrical domains with VMO…
An accurate force calculation with the Poisson-Boltzmann equation is challenging, as it requires the electric field on the molecular surface. Here, we present a calculation of the electric field on the solute-solvent interface that is exact…
Cellular electrophysiology is often modeled using the cable equations. The cable model can only be used when ionic concentration effects and three dimensional geometry effects are negligible. The Poisson model, in which the electrostatic…