Related papers: Bicomplex Schwarz and Dirichlet Boundary Value Pro…
In this paper, we show the existence of a sequence of eigenvalues for a Dirichlet problem involving two mixed fractional operators with different orders. We provide lower and upper bounds for the sum of the eigenvalues. Applications of…
We develop representations for bicomplex-valued functions in Hardy classes that generalize the complex holomorphic Hardy spaces. Using these representations, we show these functions have boundary values in the sense of distributions that…
New 2-norm bounds for solutions of planar div-curl boundary value problems on bounded planar regions are described. Prescribed flux, tangential trace and mixed boundary boundary are treated. A harmonic decomposition is used to separate…
Boundary value problems on the unit sphere arise naturally in geophysics and oceanography when scientists model a physical quantity on large scales. Robust numerical methods play an important role in solving these problems. In this article,…
We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.
In this paper we prove a Schwarz-Pick lemma for bounded complex-valued harmonic functions in the unit ball of R^n.
We develop a theory of bounded variation functions and Besov spaces in abstract Dirichlet spaces which unifies several known examples and applies to new situations, including fractals.
Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using…
The aim of this paper is to establish some properties of solutions to the Dirichlet-Neumann problem: $(\partial_z\partial_{\overline{z}})^2 w=g$ in the unit disc $\ID$, $w=\gamma_0$ and…
In this paper, we prove that there exists a unique, bounded continuous weak solution to the Dirichlet boundary value problem for a general class of second-order elliptic operators with singular coefficients, which does not necessarily have…
In this note we devise and analyze a well-posed variational formulation of the Neumann boundary value problem associated to the biharmonic operator $\Delta^2$. An alternative formulation as a system of two Poisson problems for the Laplace…
We develop a new approach to the invertibility of the layer potentials on $L^p$ associated with elliptic equations and systems in Lipschitz domains. As a consequence, for $n\ge 4$ and $(2(n-1)/(n+1))-\epsilon<p<2$, we obtain the solvability…
Using critical point theory methods we undertake the existence and multiplicity of solutions for discrete anisotropic two-point boundary value problems.
We study properties of pseudodifferential operators which arise in their use in boundary value problems. Smooth domains as well as intersections of smooth domains are considered.
It is developed the theory of the Dirichlet problem for harmonic functions. On this basis, for the nondegenerate Beltrami equations in the quasidisks and, in particular, in the smooth domains, it is proved the existence of regular solutions…
We solve the Dirichlet problem for $k$-Hessian equations on compact complex manifolds with boundary, given the existence of a subsolution. Our method is based on a second order a priori estimate of the solution on the boundary with a…
In the presented work, we solve the Dirichlet boundary problem for the Helmholtz equation in an exterior angle with periodic boundary data. We prove the existence and uniqueness of solution in an appropriate funcional class and we give an…
It is shown that the non-homogeneous Dirichlet and Neuman problems for the $2^{nd}$-order Seiberg-Witten equation admit a regular solution once the $\mathcal{H}$-condition (described in the article) is satisfied. The approach consist in…
In this article, Bohr type inequalities for some complex valued harmonic functions defined on the unit disk are given. All the results are sharp.
The aim of this paper is to obtain the existence of solution for the fractional p-Laplacian Dirichlet problem with mixed derivatives \begin{eqnarray*} &{_{t}}D_{T}^{\alpha}\left(|_{0}D_{t}^{\alpha}u(t))|^{p-2}{_{0}}D_{t}^{\alpha}u(t)\right)…