Related papers: Newton's second law with a semiconvex potential
We apply a simple decomposition to the energy of a moving particle. Based on this decomposition, we identify the potential and kinetic energies, then use them to give general definitions of momentum and the various kinds of forces exerted…
We consider the Dirichlet and Neumann problems for second-order linear elliptic equations: \[ -\triangle u +\mathrm{div}(u\mathbf{b}) =f \quad\text{ and }\quad -\triangle v -\mathbf{b} \cdot \nabla v =g \] in a bounded Lipschitz domain…
We extend the known consistency conditions on the low-energy theory of six-dimensional N = 1 supergravity. We review some facts about the theory of two-form gauge fields and conclude that the charge lattice Gamma for such a theory has to be…
This is a sequel to [1] and [2], which study the second boundary problem for special Lagrangian curvature potential equation. As consequences, we obtain the existence and uniqueness of the smooth uniformly convex solution by the method of…
We consider the compressible isentropic Euler equations on $\mathbb{T}^d\times [0,T]$ with a pressure law $p\in C^{1,\gamma-1}$, where $1\le \gamma <2$. This includes all physically relevant cases, e.g.\ the monoatomic gas. We investigate…
By applying the generalized second law to the apparent horizon of a homogeneous and isotropic universe and imposing that the equation of state is no less than $-1$, it is seen that universes with either flat or closed spatial sections are…
The supersymmetric approach in the form of second order intertwining relations is used to prove the exact solvability of two-dimensional Schrodinger equation with generalized two-dimensional Morse potential for $a_0=-1/2$. This…
We derive the Maxwell's equations on the $\kappa$-deformed spacetime, valid up to first order in the deformation parameter, using the Feynman's approach. We show that the electric-magnetic duality is a symmetry of these equations. It is…
This paper offers a number of examples showing that in the case of two independent variables the uniform ellipticity of a linear system of differential equations with partial derivatives of the second order, which fulfills condition (3), do…
We consider solutions of two-dimensional $m \times m$ systems hyperbolic conservation laws that are constant in time and along rays starting at the origin. The solutions are assumed to be small $L^\infty$ perturbations of a constant state…
In this paper we consider the stability for a type of stochastic McKean-Vlasov equations with non-Lipschitz coefficients. First, sufficient conditions are given for the exponential stability of the second moments for their solutions in…
We consider the comparison principle for semicontinuous viscosity sub- and supersolutions of second order elliptic equations on the form $F(D^2 w,x) = 0$. A structural condition on the operator is presented that seems to unify the different…
The thermodynamic behaviour of a relativistic perfect simple fluid obeying the equation of state $p=(\gamma-1)\rho $, where $0 \le \gamma \le 2$ is a constant, has been investigated. Particular cases include: vacuum($p=-\rho $, $\gamma=0$),…
The main objective of the paper is to determine asymptotic solutions to the initial-value conditions for Vlasov-Ampere/Gauss system of equations that is to find the "far field" solutions. Next, we determine dispersion relations for…
We discuss some outstanding open questions regarding the validity and uniqueness of the standard second order Newton-Einstein classical gravitational theory. On the observational side we discuss the degree to which the realm of validity of…
The electrostatic potential in a superconductor is studied. To this end Bardeen's extension of the Ginzburg-Landau theory to low temperatures is used to derive three Ginzburg-Landau equations - the Maxwell equation for the vector potential,…
This paper establishes an existence theory for distributed periodic solutions to Newton's equation with stochastic time-periodic forcing, where the friction matrix is the Hessian of a twice continuously differentiable friction function.…
The density profiles and other quantities of physical interest for spherically symmetric systems are computed by assuming that a collisionless stellar gas may relax to the non-Gaussian power law distribution suggested by the nonextensive…
Extending the results of Nardi (2015), this note establishes an existence and uniqueness result for second-order uniformly elliptic PDEs in divergence form with Neumann boundary conditions. A Schauder estimate is also derived.
We find new Melvin-like solutions in Einstein-Maxwell-dilaton gravity with a Liouville-type dilaton potential. The properties of the corresponding solution in Freedman-Schwarz gauged supergravity model are extensively studied. We show that…