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On Lp- Lr Estimates for the Wave-Equation
TLDR
In this article, the authors present a short proof of some of the results announced by Littman [4], and in particular to obtain a fundamental Lp-Lp, estimate for a class of evolution equations with constant coefficients, in particular containing the stimate for the wave-equation due to Strichartz.Abstract:
The purpose of this note is to present a short proof of some of the results announced by Littman [4], and in particular to obtain a fundamental Lp-Lp , estimate for a class of evolution equations with constant coefficients, in particular containing the stimate for the wave-equation due to Strichartz [-7, 8]. The method used here is particularly apt to deal with approximations to the wave-equation, such as those obtained by finite element or finite difference methods. Details of such applications will appear elsewhere.read more
Citations
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Journal Article
Generalized strichartz inequalities for the wave equation
J. Ginibre,Giorgio Velo +1 more
TL;DR: Strichartz inequalities for the wave equation are estimates of the solution u of the Cauchy problem for that equation, in the form of space-time integral norms, in terms of similar norms of the inhomogeneity f and of suitable norm of the initial data.
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The Global Cauchy Problem for the Non Linear Klein-Gordon Equation.
Jean Ginibre,Giorgio Velo +1 more
TL;DR: On demontre l'unicite de solutions faibles et l'existence and l'uniformity de solutions globales fortement continues dans l'espace energie as mentioned in this paper.
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Smoothing properties and retarded estimates for some dispersive evolution equations
J. Ginibre,Giorgio Velo +1 more
TL;DR: In this article, a general formulation for dispersive evolution equations is presented, which makes the separation between the two types of ingredients as clear as possible, and illustrate it with the examples of the Schrodinger equation, of the wave equation, and of a class of 1+1 dimensional equations related to the Benjamin-Ono equation.
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Lp estimates for the wave equation
TL;DR: In this article, it was shown that the linear operator T is bounded in Lp if and only if α = 1 −(n − 1) ¦ p −1 − 2 −1 ¦ > (n −1) −1.
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Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation
Daniel Tataru,Daniel Tataru +1 more
TL;DR: In this paper, the wave equation in the hyperbolic space HI and the Strichartz type estimates in the Minkowski space were obtained. But the results of Georgiev, Lindblad and Sogge on global existence for solutions to semilinear HH problems with small data were not discussed.
References
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Convolutions with kernels having singularities on a sphere
TL;DR: In this paper, it was shown that convolution with (1xI2)+ and related convolutions are bounded from LI to Lq for certain values of p and q, and that p is a unique choice of p which maximizes the measure of smoothing.
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Fourier transforms of surface-carried measures and differentiability of surface averages
TL;DR: In this paper, the authors studied the behavior of the Fourier transform of the measure p. The main result in that direction is the following: ESTIMATE OF FOURIER TRANSFORMS.
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Besov spaces in theory of approximation
TL;DR: In this article, the authors apply the theory of interpolation spaces to different parts of approximation theory and study the rate of convergence of summation processes of Fourier series and Fourier integrals.
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