Related papers: A solution to the Pompeiu problem

A classical result of F.Klein states that, given a finite primitive group $G\subseteq SL_2(\mathbb{C})$, there exists a hypergeometric equation such that any second order LODE whose differential Galois group is isomorphic to $G$ is…

We prove that, if $g$ is a continuous asymptotically convex function, any solution $u$ of $-\Delta u+g(u)=0$ in a ball B which tends to infinity on $\partial B$ is radially symmetric.

We consider density solutions for gradient flow equations of the form $u_t = \nabla \cdot ( \gamma(u) \nabla \mathrm N(u))$, where $\mathrm N$ is the Newtonian repulsive potential in the whole space $\mathbb R^d$ with the nonlinear convex…

In this paper we present a survey concerning unconstrained free boundary problems of type $$ \left\{ \begin{array}{ll} F_1(D^2u,\nabla u,u,x)=0 & \text{in }B_1 \cap \Omega ,\\ F_2 (D^2 u,\nabla u,u,x)=0 & \text{in }B_1\setminus\Omega ,\\ u…

To any non-negatively graded dg Lie algebra $g$ over a field $k$ of characteristic zero we assign a functor $\Sigma_g: art/k \to Kan$ from the category of commutative local artinian $k$-algebras with the residue field $k$ to the category of…

In this paper the results of Radloff and Schwabe (2019a) will be extended for a special class of symmetrical intensity functions. This includes binary response models with logit and probit link. To evaluate the position and the weights of…

We analyze the possibility of description of D-dimensional massless particles by the Lagrangians linear on world-line curvatures k_i, {\cal S}=\sum_{i=1}^Nc_i\int k_i d{\tilde s}. We show, that the nontrivial classical solutions of this…

In this note, we consider the following problem, \begin{equation*} \begin{cases} -\Delta u=(1+g(x))u^{\frac{N+2}{N-2}},\ u>0\text{ in }B,\\ u=0\text{ on }\partial B, \end{cases} \end{equation*} where $N\ge3$ and $B\subset \mathbb{R}^N$ is a…

The Milnor Problem (modified) in the theory of group growth asks whether any finite presented group of vanishing algebraic entropy has at most polynomial growth. We show that a positive answer to the Milnor Problem (modified) is equivalent…

Several N-body problems in ordinary (3-dimensional) space are introduced which are characterized by Newtonian equations of motion (``acceleration equal force;'' in most cases, the forces are velocity-dependent) and are amenable to exact…

We consider Schubert problems with respect to flags osculating the rational normal curve. These problems are of special interest when the osculation points are all real -- in this case, for zero-dimensional Schubert problems, the solutions…

A new approach to Nori's weak Lefschetz theorem is described. The new approach, which involves the dbar-method, avoids moving arguments and gives much stronger results. In particular, it is proved that if X and Y are connected smooth…

We prove the uniform boundedness of all solutions for a general class of Dirichlet anisotropic elliptic problems of the form $$-\Delta_{\overrightarrow{p}}u+\Phi_0(u,\nabla u)=\Psi(u,\nabla u) +f $$ on a bounded open subset $\Omega\subset…

It is commonly accepted that general relativity is the only solution to the consistency problem that appears when trying to build a theory of interacting gravitons (massless spin-2 particles). Padmanabhan's 2008 thought-provoking analysis…

In this paper a fluid-structure interaction problem for the incompressible Newtonian fluid is studied. We prove the convergence of an iterative process with respect to the computational domain geometry. In our previous works on numerical…

For an algebraically closed field $\mathbb{K}$, we consider a Galois $G$-covering $\mathcal{B} \to \mathcal{A}$ between locally bounded $\mathbb{K}$-categories given by bound quivers, where $G$ is torsion-free and acts freely on the objects…

We study the critical Neumann problem \begin{equation*} \begin{cases} -\Delta u = |u|^{2^*-2}u &\text{in }\Sigma_\omega,\\ \quad\frac{\partial u}{\partial\nu}=0 &\text{on }\partial\Sigma_\omega, \end{cases} \end{equation*} in the unbounded…

Generalized Pauli's theorem, proved by D. S. Shirokov for two sets of anticommuting elements of a real or complexified Clifford algebra of dimension $2^n$, is extended to the case, when both sets of elements depend smoothly on points of…

We derive a 4D covariant Relativistic Dynamics Equation. This equation canonically extends the 3D relativistic dynamics equation $\mathbf{F}=\frac{d\mathbf{p}}{dt}$, where $\mathbf{F}$ is the 3D force and $\mathbf{p}=m_0\gamma\mathbf{v}$ is…

It is a classical result that if $u \in C^2(\mathbb{R}^n;\mathbb{R}^n)$ and $\nabla u \in SO(n)$ it follows that $u$ is rigid. In this article this result is generalized to matrix fields with non-vanishing curl. It is shown that every…