A note on a 3-dimensional stationary Schrödinger-Poisson system.
A note on a critical problem with natural growth in the gradient
The paper analyzes the influence on the meaning of natural growth in the gradient of a perturbation by a Hardy potential in some elliptic equations. Indeed, in the case of the Laplacian the natural problem becomes in , on , . This problem is a particular case of problem (2). Notice that is optimal as coefficient and exponent on the right hand side.
A note on a degenerate elliptic equation with applications for lakes and seas.
A note on a discrete form of Friedrichs' inequality
The proof of the Friedrichs' inequality on the class of finite dimensional spaces used in the finite element method is given. In particular, the approximate spaces generated by simplicial isoparametric elements are considered.
A note on a heat potential and the parabolic variation
A note on a Liouville-type result for a system of fourth-order equations in .
A note on a theorem of Jörgens.
A Note on an Application of the Lasota-York Fixed Point Theorem in the Turbulent Transport Problem
We study a model of motion of a passive tracer particle in a turbulent flow that is strongly mixing in time variable. In [8] we have shown that there exists a probability measure equivalent to the underlying physical probability under which the quasi-Lagrangian velocity process, i.e. the velocity of the flow observed from the vintage point of the moving particle, is stationary and ergodic. As a consequence, we proved the existence of the mean of the quasi-Lagrangian velocity, the so-called Stokes...
A note on asymptotic expansion for a periodic boundary condition
The aim of this contribution is to present a new result concerning asymptotic expansion of solutions of the heat equation with periodic Dirichlet–Neuman boundary conditions with the period going to zero in D.
A note on asymptotic helix and quantum mechanical structure.
A note on bounds for non-linear multivalued homogenized operators
In this paper we study the behaviour of maximal monotone multivalued highly oscillatory operators. We construct Reuss-Voigt-Wiener and Hashin-Shtrikmann type bounds for the minimal sections of G-limits of multivalued operators by using variational convergence and convex analysis.
A note on Chebyshev series solution of the Crank-Gupta equation.
A note on continuity of pseudodifferential operators in Hardy spaces.
A note on critical times of quasilinear hyperbolic systems
In this paper the exact formula for the critical time of generating discontinuity (shock wave) in a solution of a quasilinear hyperbolic system is derived. The applicability of the formula in the engineering praxis is shown on one-dimensional equations of isentropic non-viscous compressible fluid flow.
A Note on Div-Curl Lemma
2000 Mathematics Subject Classification: 42B30, 46E35, 35B65.We prove two results concerning the div-curl lemma without assuming any sort of exact cancellation, namely the divergence and curl need not be zero, and which include as a particular case, the result of [3].
A note on Hayman's theorem on the bass note of a drum.
A note on hyperbolic partial differential equations. II.
A note on Krylov's -theory for systems of SPDEs.
A note on lifting of Carnot groups.
We prove that every homogeneous Carnot group can be lifted to a free homogeneous Carnot group. Though following the ideas of Rothschild and Stein, we give simple and self-contained arguments, providing a constructive proof, as shown in the examples.
A note on local smoothing effects for the unitary group associated with the KdV equation.