000			02785nam a22003015i 4500
001			65678
005			20200415112305.0
010			_a978-3-0348-0840-8 _dcompra
090			_a65678
100			_a20150401d2014 k||y0pory50 ba
101			_aeng
102			_aCH
200			_aVariable Lebesgue spaces and hyperbolic systems _bDocumento electrónico _fDavid Cruz-Uribe ... [et al.] _gedited by Sergey Tikhonov
210			_aBasel _cSpringer _cBirkhäuser _d2014
215			_aIX, 170 p. _cil.
225			_aAdvanced Courses in Mathematics _eCRM Barcelona
303			_aThis book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function space properties of variable Lebesgue spaces; proofs are modeled on the classical theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such as convolution operators and singular integrals. The text is mostly self-contained, with only some more technical proofs and background material omitted. Part 2 gives an overview of the asymptotic properties of solutions to hyperbolic equations and systems with time-dependent coefficients. First, an overview of known results is given for general scalar hyperbolic equations of higher order with constant coefficients. Then strongly hyperbolic systems with time-dependent coefficients are considered. A feature of the described approach is that oscillations in coefficients are allowed. Propagators for the Cauchy problems are constructed as oscillatory integrals by working in appropriate time-frequency symbol classes. A number of examples is considered and the sharpness of results is discussed. An exemplary treatment of dissipative terms shows how effective lower order terms can change asymptotic properties and thus complements the exposition.
606			_aIntegrais de Lebesgue
606			_aEquações diferenciais hiperbólicas
680			_aQA36
701			_4070 _aCruz-Uribe _bDavid
702			_aTikhonov _bSergey _4340
801			_aPT _gRPC
856			_uhttp://dx.doi.org/10.1007/978-3-0348-0840-8
942			_2lcc _cF _n0