Integral Kernel Estimates for a Linear Singular Operator Linked with Boltzmann Equation Part I: Small Singularities 0 < Ν < 1 and Besov to L P Estimates
نویسنده
چکیده
where the unknown f(t, x, v) is a nonnegative integrable function standing for the density of particles in phase space : time t ≥ 0, position x ∈ R, velocity v ∈ R, n ≥ 2. More precisely, this first part is devoted to some properties linked with the operator from (1.13) below, which is linked with one possible weak formulation of Boltzmann equation (1.1). On the right hand side of (1.1), Q is the Boltzmann collision operator, which acts only on the velocity dependence of f
منابع مشابه
Integral Kernel Estimates for a Linear Singular Operator Linked with Boltzmann Equation Part 2: Small Singularities 0 < Ν < 1 and Regularity Issues
In this work, we continue the study of precise functional properties of a linear operator linked with Boltzmann quadratic operator, started in Part I. This is done for singular cross-sections. In particular, we show Calderon-Zygmund type estimates.
متن کاملWavelet-based numerical method for solving fractional integro-differential equation with a weakly singular kernel
This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular kernel. First, a collocation method based on Haar wavelets (HW), Legendre wavelet (LW), Chebyshev wavelets (CHW), second kind Chebyshev wavelets (SKCHW), Cos and Sin wavelets (CASW) and BPFs are presented f...
متن کاملA finite difference method for the smooth solution of linear Volterra integral equations
The present paper proposes a fast numerical method for the linear Volterra integral equations withregular and weakly singular kernels having smooth solutions. This method is based on the approx-imation of the kernel, to simplify the integral operator and then discretization of the simpliedoperator using a forward dierence formula. To analyze and verify the accuracy of the method, weexamine samp...
متن کاملWeighted Norm Inequalities, Off-diagonal Estimates and Elliptic Operators Part I: General Operator Theory and Weights Pascal Auscher and José
This is the first part of a series of four articles. In this work, we are interested in weighted norm estimates. We put the emphasis on two results of different nature: one is based on a good-λ inequality with two parameters and the other uses Calderón-Zygmund decomposition. These results apply well to singular “non-integral” operators and their commutators with bounded mean oscillation functio...
متن کاملAdaptive Methods for Semi-linear Elliptic Equations with Critical Exponents and Interior Singularities Adaptive Methods for Semi-linear Elliptic Equations with Critical Exponents and Interior Singularities
We consider the eeectiveness of adaptive nite-element methods for nding the nite element solutions of the parametrised semi-linear elliptic equation u+u+u 5 = 0; u > 0, where u 2 C 2 ((); for a domain IR 3 and u = 0 on the boundary of : This equation is important in analysis and it is known that there is a value 0 > 0 such that no solutions exist for < 0 and a singularity forms as ! 0. Furtherm...
متن کامل