Related papers: Monogenic functions in the biharmonic boundary val…
We consider functions which are subfunctions with respect to the differential operator $$L_\rho = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + 2\rho \frac{\partial}{\partial x} + \rho^2 $$ and are doubly periodic in…
In this paper we study an inverse boundary value problem for the biharmonic operator with first order perturbation. Our geometric setting is that of a bounded simply connected domain in the Euclidean space of dimension three or higher.…
In this paper, we establish a boundary Schwarz lemma for solutions to non-homogeneous biharmonic equations.
We define a class of boundary value problems on manifolds with fibered boundary. This class is in a certain sense a deformation between the classical boundary value problems and the Atiyah-Patodi-Singer problems in subspaces. The boundary…
We consider the Dirichlet problem for the biharmonic equation on an arbitrary convex domain and prove that the second derivatives of the variational solution are bounded in all dimensions.
The paper considers a boundary value problem for the high-order Lavrent'ev-Bitsadze equation. Necessary and sufficient conditions for the uniqueness of the solution are found. When substantiating the existence, the problem of "small…
For a bounded weak Lipschitz domain we show the so called `Maxwell compactness property', that is, the space of square integrable vector fields having square integrable weak rotation and divergence and satisfying mixed tangential and normal…
We consider second order uniformly elliptic operators of divergence form in $\R^{d+1}$ whose coefficients are independent of one variable. For such a class of operators we establish a factorization into a product of first order operators…
Let $\Omega\subset \Bbb R^2$ be a bounded domain with $\partial\Omega\in C^\infty$ and $L$ be a positive number. For a three dimensional cylindrical domain $Q=\Omega\times (0,L)$, we obtain some uniqueness result of determining a…
Cauchy Biorthogonal Polynomials appear in the study of special solutions to the dispersive nonlinear partial differential equation called the Degasperis-Procesi (DP) equation, as well as in certain two-matrix random matrix models. Another…
We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic…
We extend representation formulas that generalize the similarity principle of solutions to the Vekua equation to certain classes of meta-analytic functions. Also, we solve a generalization of the higher-order Schwarz boundary value problem…
Fractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping…
This paper studies a Sturm--Liouville boundary value problem in which one of the boundary conditions depends bilinearly on the spectral parameter. The differential equation is considered on the interval $(0,1)$ with a classical boundary…
We study existence of solutions for a boundary degenerate (or singular) quasilinear equation in a smooth bounded domain under Dirichlet boundary conditions. We consider a weighted $p-${L}aplacian operator with a coefficient that is {locally…
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the…
In this paper, we study the existence of nontrivial solutions of the Dirichlet boundary value problem for the following elliptic system: \begin{equation} \left\{ \begin{aligned} -\Delta u & = au + bv + f(x,u,v); &\quad\mbox{ for…
In this paper, we study the Bohr phenomenon for functions that are defined on a general simply connected domain of the complex plane. We improve known results of R. Fournier and St. Ruscheweyh for a class of analytic functions. Furthermore,…
Let D be a smoothly bounded domain in complex space of dimension larger than 2. Suppose that D admits a smooth defining function which is plurisubharmonic on the boundary of D. Then the Diederich-Fornaess exponent can be chosen arbitrarily…
A rigorous methodology for the analysis of initial boundary value problems on the half-line, $0<x<\infty$, $t>0$, for integrable nonlinear evolution PDEs has recently appeared in the literature. As an application of this methodology the…