Maximal Regularity for Flexible Structural Systems in Lebesgue Spaces
نویسندگان
چکیده
We study abstract equations of the form λu′′′ t u′′ t c2Au t c2μAu′ t f t , 0 < λ < μ which is motivated by the study of vibrations of flexible structures possessing internal material damping. We introduce the notion of α; β; γ -regularized families, which is a particular case of a; k regularized families, and characterize maximal regularity in L-spaces based on the technique of Fourier multipliers. Finally, an application with the Dirichlet-Laplacian in a bounded smooth domain is given.
منابع مشابه
L–regularity for Parabolic Operators with Unbounded Time–dependent Coefficients
We establish the maximal regularity for nonautonomous OrnsteinUhlenbeck operators in L-spaces with respect to a family of invariant measures, where p ∈ (1,+∞). This result follows from the maximal L-regularity for a class of elliptic operators with unbounded, time-dependent drift coefficients and potentials acting on L(R ) with Lebesgue measure.
متن کاملOn isomorphism of two bases in Morrey-Lebesgue type spaces
Double system of exponents with complex-valued coefficients is considered. Under some conditions on the coefficients, we prove that if this system forms a basis for the Morrey-Lebesgue type space on $left[-pi , pi right]$, then it is isomorphic to the classical system of exponents in this space.
متن کاملMultilinear Fourier Multipliers with Minimal Sobolev Regularity
Letm be a positive integer. In this talk, we will introduce optimal conditions,expressed in terms of Sobolev spaces, on m-linear Fourier multiplier operatorsto be bounded from a product of Lebesgue or Hardy spaces to Lebesgue spaces.Our results are sharp and cover the bilinear case (m = 2) obtained by Miyachiand Tomita [1]. References[1] Miyachi A., and Tomita N., Minima...
متن کاملAlmost Critical Well-posedness for Nonlinear Wave Equations with Qμν Null Forms in 2d
In this paper we prove an optimal local well-posedness result for the 1+2 dimensional system of nonlinear wave equations (NLW) with quadratic null-form derivative nonlinearities Qμν . The Cauchy problem for these equations is known to be ill-posed for data in the Sobolev space H with s ≤ 5/4 for all the basic null-forms, except Q0, thus leaving a gap to the critical regularity of sc = 1. Follow...
متن کاملMaximal inequalities for dual Sobolev spaces W − 1 , p and applications to interpolation
We firstly describe a maximal inequality for dual Sobolev spaces W−1,p. This one corresponds to a “Sobolev version” of usual properties of the Hardy-Littlewood maximal operator in Lebesgue spaces. Even in the euclidean space, this one seems to be new and we develop arguments in the general framework of Riemannian manifold. Then we present an application to obtain interpolation results for Sobol...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010