On the penalized obstacle problem in the unit half ball.
On the periodic KdV equation in weighted Sobolev spaces
On the persistence of decorrelation in the theory of wave turbulence
We study the statistical properties of the solutions of the Kadomstev-Petviashvili equations (KP-I and KP-II) on the torus when the initial datum is a random variable. We give ourselves a random variable with values in the Sobolev space with big enough such that its Fourier coefficients are independent from each other. We assume that the laws of these Fourier coefficients are invariant under multiplication by for all . We investigate about the persistence of the decorrelation between the...
On the perturbation propagation in the initial-boundary value problem for quasilinear first order equations.
The paper deals with initial-boundary value problem for generalized solutions of single quasilinear nonautonomous conservation law. For the case so-called "processes with aggravation" the localization property and inner boundedness are studied. Also in case when boundary function tends to zero as t ⇒ +∞ the localization effect is regarded.
On the Picard problem for hyperbolic differential equations in Banach spaces
B. Rzepecki in [5] examined the Darboux problem for the hyperbolic equation on the quarter-plane x ≥ 0, y ≥ 0 via a fixed point theorem of B.N. Sadovskii [6]. The aim of this paper is to study the Picard problem for the hyperbolic equation using a method developed by A. Ambrosetti [1], K. Goebel and W. Rzymowski [2] and B. Rzepecki [5].
On the Plasma-Charge problem
This short report is a review on recent results of S. Caprino, C. Marchioro, E. Miot and the author on the initial value problem associated to the evolution of a continuous distribution of charges (plasma) in presence of a finite number of point charges.
On the point limit of the Pauli-Fierz model
On the point spectrum of Schrödinger operators
On the poles of the scattering matrix for two convex obstacles
On the positivity of an invariant measure on open non-empty sets
On the precise asymptotics of the constant in Friedrich's inequality for functions vanishing on the part of the boundary with microinhomogeneous structure.
On the principal eigencurve of the p-Laplacian related to the Sobolev trace embedding
We prove that for any λ ∈ ℝ, there is an increasing sequence of eigenvalues μₙ(λ) for the nonlinear boundary value problem ⎧ in Ω, ⎨ ⎩ on crtial ∂Ω and we show that the first one μ₁(λ) is simple and isolated; we also prove some results about variations of the density ϱ and the continuity with respect to the parameter λ.
On the Principal Eigenvalue of a Second Order Linear Elliptic Problem with an Indefinite Weight Function.
On the principal eigenvalue of elliptic operators in and applications
Two generalizations of the notion of principal eigenvalue for elliptic operators in are examined in this paper. We prove several results comparing these two eigenvalues in various settings: general operators in dimension one; self-adjoint operators; and “limit periodic” operators. These results apply to questions of existence and uniqueness for some semilinear problems in the whole space. We also indicate several outstanding open problems and formulate some conjectures.
On the Principal Eigenvalues of Indefinite Elliptic Problems.
On the Principle of Linearized Stability for Varitional Inequalities.
On the principle of stability of invariance of physical systems
On the problem of convergence of a bounded-below sequence of symmetric forms for the Schrödinger operators
On the problem of determining the parameters of a layered elastic medium and an impulse source.
On the problem of determining the structure of a layered medium and the shape of an impulse source.