Related papers: Regular singular Volterra equations on complex dom…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…
We present here a fine singularity analysis of solutions to the Laplace equation in special polygonal domains in the plane. We assume piecewise constant Neumann on one component of the boundary. Our motivation is to find the rigorous proof…
In this short note, we provide an elementary complex analytic method for converting known real integrals into numerous strange and interesting looking real integrals.
The Riccati equations reducible to first-order linear equations by an appropriate change the dependent variable are singled out. All these equations are integrable by quadrature. A wide class of linear ordinary differential equations…
A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The construction begins with a harmonic approximation of the…
In this paper, we investigate the inverse generator problem for abstract degenerate Volterra integro-differential equations in locally convex spaces. The classes of degenerate $(a,k)$-regularized $C$-resolvent families and degenerate mild…
We define a generalization of convex functions, which we call $\delta$-convex functions, and show they must satisfy interior H\"older and $W^{1,p}$ estimates. As an application, we consider solutions of a certain class of fully nonlinear…
The probe and singular sources methods are two well-known classical direct reconstruction methods in inverse obstacle problems governed by partial differential equations. In this paper, by considering an inverse obstacle problem governed by…
In this paper, we present a novel method to compute an explicit formula for the inverse of the confluent Vandermonde matrices. Our proposed results may have many interesting perspectives in diverse areas of mathematics and natural sciences,…
The Volterra calculus is a simple and powerful pseudodifferential tool for inverting parabolic equations and it has also found many applications in geometric analysis. On the other hand, an important property in the theory of…
In this paper, the conformable Laguerre and associated Laguerre differential equations are solved using the Laplace transform. The solution is found to be in exact agreement with that obtained using the power series. In addition some of…
Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…
We establish new weak existence results for $d$-dimensional Stochastic Volterra Equations (SVEs) with continuous coefficients and possibly singular one-dimensional non-convolution kernels. These results are obtained by introducing an…
Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…
Differential equations with infinitely many derivatives, sometimes also referred to as ``nonlocal'' differential equations, appear frequently in branches of modern physics such as string theory, gravitation and cosmology. The goal of this…
We introduce a fractional calculus on time scales using the theory of delta (or nabla) dynamic equations. The basic notions of fractional order integral and fractional order derivative on an arbitrary time scale are proposed, using the…
For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary…
We study the Hadamard finite part of divergent integrals of differential forms with singularities on submanifolds. We give formulae for the dependence of the finite part on the choice of regularization and express them in terms of a…
Mather and Yau showed that an isolated complex hypersurface singularity is completely determined by its moduli algebra. It is shown, for the simple elliptic singularities, how to construct continuous invariants from the moduli algebras and,…
We obtain new concavity results, up to a suitable transformation, for a class of quasi-linear equations in a convex domain involving the $p$-Laplace operator and a general nonlinearity satisfying concavity type assumptions. This provides an…