Related papers: A Note on the Paper "The unique solution of the ab…
This paper is concerned with solving some structured multi-linear systems, which are called tensor absolute value equations. This kind of absolute value equations is closely related to tensor complementarity problems and is a generalization…
We prove the existence and uniqueness of weak solutions to a class of anisotropic elliptic equations with coefficients of convection term belonging to some suitable Marcinkiewicz spaces. Some useful a priori estimates and regularity results…
A comment has been recently posted on the arXiv (arXiv:1902.07504) that discuss our recent work on encircling multiple exceptional points in Nat. Commun. 9, 4808 (2018). In that comment, the authors claim that our approach is prone to…
We present new proofs to four versions of Peano's Existence Theorem for ordinary differential equations and systems. We hope to have gained readability with respect to other usual proofs. We also intend to highlight some ideas due to Peano…
We present a new approach to Davie's theorem on the uniqueness of solutions to the equation $dX_t = b(t, X_t)\,dt + dW_t$ for almost all Brownian paths. A generalization of this result and a discussion of some close problems are given.
In this Note, we study a transport-diffusion equation with rough coefficients and we prove that solutions are unique in a low-regularity class.
This note covers two parts. The first one provides an errata to the paper "Numerical and analytical modeling of busbar systems". We mainly give the correction for three equations affected by a typographical mistake. Despite the corrections…
In a recent series of important works \cite{wei-zhang-1,wei-zhang-2,wei-zhang-3}, Wei-Zhang proved several vanishing theorems for non-simple blow-up solutions of singular Liouville equations. It is well known that a non-simple blow-up…
We study uniqueness of solutions to degenerate parabolic problems, posed in bounded domains, where no boundary conditions are imposed. Under suitable assumptions on the operator, uniqueness is obtained for solutions that satisfy an…
It is sometimes claimed that the twin "paradox" requires general relativity for a resolution. This paper presents a simple, exact resolution using only special relativity and the equivalence principle. Two earlier approximate solutions are…
The paper reviews rigorous results about quantum dots, in particular exact solutions for few electron dots and limit theorems for high magnetic fields and/or high electron number.
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
In this work, we show that several problems naturally represented as Nonlinear Absolute Value Equations (NAVE) can be reformulated as Nonlinear Complementarity Problems (NCP) and efficiently solved using smoothing regularization techniques…
The aim of the note is to proof a regularity result for weak solutions to the Navier-Stokes equations that are locally in $L_\infty(L^{3,\infty})$. It reads that, in a sense, the number of singular points at each time is at most finite. Our…
This paper is concerned with singular matrix difference equations of mixed order. The existence and uniqueness of initial value problems for these equations are derived, and then the classification of them is obtained with a similar…
This paper is concerned with the solvability of some abstract differential equation of type $$\dot u(t) + Au(t) + Bu(t) \ni f(t), t \in (0,T], u(0) = 0,$$ where $A$ is a linear selfadjoint operator and $B$ is a nonlinear(possibly…
We introduce a full solution to a problem considered by Wang and Chu concerning series involving the squares of finite sums of the form $1 + \frac{1}{3}+ \cdots + \frac{1}{2n-1}$. Our proof involves techniques from the theory of colored…
We explore singular second-order boundary value problems with mixed boundary conditions on a general time scale. Using the lower and upper solutions method combined with the Brouwer fixed point theorem we demonstrate the existence of a…
We revisit and slightly modify the proof of the Gaussian Hanson-Wright inequality where we keep track of the absolute constant in its formulation.
This article studies the uniqueness of the weak solution of the incompressible Navier-Stokes Equations in the 3-dimensional case. Here, the investigation is provided using two different approaches. The first (the main) result is obtained…