Velocity averaging - a general framework (CROSBI ID 589399)
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Podaci o odgovornosti
Lazar, Martin ; Mitrović, Darko
engleski
Velocity averaging - a general framework
We establish the strong $\Ldl\Rd$ precompactness of the sequence of averaged quantities $\int_{; ; \R^m}; ; u_n(\mx, \msnop)$ $\rho(\msnop)d\msnop$, where $\rho\in \Ldc{; ; \R^m}; ; $ , and $u_n\in \Ld{; ; \R^m ; \pL s\Rd}; ; $, $s\geq 2$, are weak solutions to differential operator equations with variable coefficients. In particular, this includes differential operators of hyperbolic, parabolic or ultraparabolic type, but also fractional differential operators. If $s>2$ then the coefficients can be discontinuous with respect to the space variable $\mx\in \R^d$. The main tool in the work is an extension of the H-measures, for which a representation theorem is proved. An application is give n to ultraparabolic equations with discontinuous coefficients.
velocity averaging; generalised H-measures; ultraparabolic equations; discontinuous coefficients
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Podaci o prilogu
23-23.
2012.
objavljeno
Podaci o matičnoj publikaciji
Topis in PDE, Microlocal and Time-frequency Analysis (PDEMTA2012) : Book of Abstracts
Novi Sad: Department of Mathematics and Informatics, University of Novi Sad
Podaci o skupu
Topis in PDE, Microlocal and Time-frequency Analysis
predavanje
03.09.2012-08.09.2012
Novi Sad, Srbija