Related papers: The Goursat problem for a generalized Helmholz ope…
We study uniqueness of Dirichlet problems of second order divergence-form elliptic systems with transversally independent coefficients on the upper half-space in absence of regularity of solutions. To this end, we develop a substitute for…
This paper investigates a nonlocal boundary value problem for a multi-parametric integral-differential equation involving the Caputo-Prabhakar type operator in a bounded rectangular domain. The nonlocal conditions are given as partial…
We study a nonlinear elliptic boundary value problem defined on a smooth bounded domain involving the fractional Laplace operator, a concave-convex powers term together with mixed Dirichlet-Neumann boundary conditions.
We prove the backward uniqueness for general parabolic operators of second order in the whole space under assumptions that the leading coefficients of the operator are Lipschitz and their gradients satisfy certain decay conditions. This…
We employ a variational approach to study the Neumann boundary value problem for the $p$-Laplacian on bounded smooth-enough domains in the metric setting, and show that solutions exist and are bounded. The boundary data considered are Borel…
Formal Laplace operators are analyzed for a large class of resistance networks with vertex weights. The graphs are completed with respect to the minimal resistance path metric. Compactness and a novel connectivity hypothesis for the…
A numerical scheme is developed for solution of the Goursat problem for a class of nonlinear hyperbolic systems with an arbitrary number of independent variables. Convergence results are proved for this difference scheme. These results are…
In this paper we consider an obstacle problem for a generalization of the p-elastic energy among graphical curves with fixed ends. Taking into account that the Euler--Lagrange equation has a degeneracy, we address the question whether…
In this paper, we consider periodic boundary value problems for differential equations whose coefficients are trigonometric polynomials. We construct the spaces of generalized functions, where such problems have solutions. In particular,…
We consider a classical problem of Computer Algebra: symbolic solution of PDEs. We transform the famous Darboux theorems on differential transformations of hyperbolic operator into the space of invariants. We introduce a new idea -- $X$-…
In this paper, we introduce a new class of confluent hypergeometric functions of many variables, study their properties, and determine a system of partial differential equations that this function satisfies. It turns out that all the…
We have studied possible applications of a particular pseudo-differential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The…
We provide necessary and sufficient conditions on the derived type of a vector field distribution $\Cal V$ in order that it be locally equivalent to a partial prolongation of the contact distribution $\Cal C^{(1)}_q$, on the first order jet…
In Trefftz discontinuous Galerkin methods a partial differential equation is discretized using discontinuous shape functions that are chosen to be elementwise in the kernel of the corresponding differential operator. We propose a new…
We study a certain one dimensional, degenerate parabolic partial differential equation with a boundary condition which arises in pricing of Asian options. Due to degeneracy of the partial differential operator and the non-smooth boundary…
For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…
We summarize the properties of eigenvalues and eigenfunctions of the Laplace operator in bounded Euclidean domains with Dirichlet, Neumann or Robin boundary condition. We keep the presentation at a level accessible to scientists from…
The present paper pioneers the study of the Dirichlet problem with $L^q$ boundary data for second order operators with complex coefficients in domains with lower dimensional boundaries, e.g., in $\Omega := \mathbb R^n \setminus \mathbb R^d$…
We study the Dirichlet problem at infinity on a Cartan-Hadamard manifold for a large class of operators containing in particular the p-Laplacian and the minimal graph operator.
We solve the Kato square root problem for parabolic operators of arbitrary order $2m$ whose coefficients are allowed to depend on both space and time in a merely measurable way and possess boundedness and ellipticity controlled by a…