Download Nonlinear Evolution Equations and Related Topics: Dedicated by Wolfgang Arendt, Haim Brezis, Michel Pierre PDF

By Wolfgang Arendt, Haim Brezis, Michel Pierre

Philippe Bénilan used to be a most unusual and charismatic mathematician who had a deep and decisive effect at the conception of nonlinear evolution equations. the current quantity is devoted to him and comprises study papers written by means of hugely amazing mathematicians. they're all concerning Bénilan's paintings and mirror the current country of this so much lively box. The contributions hide a variety of nonlinear and linear equations. specified themes are Hamilton-Jacobi equations, the porous medium equation, response diffusion structures, integro-differential equations and visco-elasticity, maximal regularity for elliptic and parabolic equations, and the Ornstein-Uhlenbeck operator.

Also during this quantity, the mythical paintings of Bénilan-Brézis on Thomas-Fermi idea is released for the 1st time.

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Extra info for Nonlinear Evolution Equations and Related Topics: Dedicated to Philippe Bénilan

Example text

Pi! 5. Let B be as in the previous proposition. H -Lipschitz continuous and L H (pff) S 1. e. Proof Clearly pff (x) < +00 if and only if x E B + H. L-negligible. Set now cp(x) = pff (x) if x E B + Hand cp(x) = 0 if x ~ B + H. We have "Ix E X 'Vh E H Icp(x +h) - cp(x)1 which yields the result. equ. 1, for A, BEn, PI! (A, B) = inf{pl! (x, y) : x E A, y E B}, and pH (A, B) = sup{pl! (A', B') : A' '" A, B' '" B}. 3, pH is a measurable pseudometric. 6. For any A, BEn, pH (A, B) = p(A, B). Proof Let first f E "Ix E R Vh E H li(x i of f lDl oo with r(f) s 1.

DAUTRAY, R. and LIONS, J. , Analyse mathematique et calcul numerique pour les sciences et les techniques, vol. 3, with the collaboration of Philippe Benilan, Michel Cessenat, Bertrand Mercier and Claude Zuily, Masson, Paris, 1987. GILDING, B. , GUEDDA, M. , The Cauchy problem for Ut = I'lu + l'Vu Iq, prepublication LAMFA 28, Universite de Picardie, 1998. LAURENyOT, PH. , On the growth of mass for a viscous Hamilton-Jacobi equation, J. Anal. , to appear. equ. 3 (2003) 39 - 65 1424-3199/03/010039 - 27 © Birkhliuser Verlag, Basel, 2003 Journal of Evolution Equations The Cauchy problem for linear growth functionals F.

1) where Uo E Lloc(JRN) anda(x,~) = Vd(x, ~), f : JRN x JRN -+ JR being a function with linear growth as II~ I -+ 00 satisfying some additional assumptions we shall precise below. 1) is the wellknown mean-curvature operator. , when f (0 = II~ II is not covered by our results. This case has been recently studied by G. Bellettini, V. Caselles andM. Novaga in [8]. 1) has been studied in [3] and [4] (see also [18], [II] and [IS]). 1), for which existence and uniqueness for initial data in Lloc(JRN) is proved.

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