By Andrew Acker (auth.), Catherine Bandle, Henri Berestycki, Bernard Brighi, Alain Brillard, Michel Chipot, Jean-Michel Coron, Carlo Sbordone, Itai Shafrir, Vanda Valente, Giorgio Vergara Caffarelli (eds.)

ISBN-10: 3764372494

ISBN-13: 9783764372491

ISBN-10: 3764373849

ISBN-13: 9783764373849

This quantity comprises contributions by means of former scholars and collaborators of Haim Brezis given in honor of his sixtieth anniversary at a convention in Gaeta. H. Brezis has made major contributions within the fields of partial differential equations and practical research. he's an inspiring instructor and counselor of many mathematicians within the entrance ranks. the gathering of papers awarded the following grew out from his deep perception of study. additionally it displays Brezis's dependent method of artistic thinking.

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**Extra resources for Elliptic and Parabolic Problems: A Special Tribute to the Work of Haim Brezis**

**Sample text**

In particular, the technique introduced in reference [2] applies here. For an alternative technique see [8]. As in [4], we illustrate the core of the proof by considering the problem in the half-space. In this case the set of points for which x3 = 0 correspond to the boundary of Ω. In the half-space case the fact that the canonical inclusions Lp1 → Lp0 , p0 < p1 , fails leads to additional technicalities and heavier notation. To avoid here this situation (regularity has a local character) assume for convenience that our + solution u has compact support in a half-sphere BR = {x : |x| < R, x3 ≥ 0}, for some R > 0.

Berm´ udez, R. C. Mu˜ niz and F. es Progress in Nonlinear Diﬀerential Equations and Their Applications, Vol. 63, 43–50 c 2005 Birkh¨ auser Verlag Basel/Switzerland A Decay Result for a Quasilinear Parabolic System Said Berrimi and Salim A. Messaoudi Dedicated to Pr. Haim. Brezis on the occasion of his 60th birthday Abstract. We show that, for suitable initial datum, the energy of the solution decays “ in time” exponentially if m = 2 whereas the decay is of a polynomial order if m > 2. Mathematics Subject Classiﬁcation (2000).

The ﬁrst bifurcation point Q = Q2 is the one most physically relevant (all the other branches should be unstable). We ﬁnally discuss the stability along the bifurcation branch emanating from Q2 and obtain the result represented in Figure 1. Finally, in Section 3 we solve numerically the evolution problem in a Stokes ﬂow. Figure 1. Graphical representation of the bifurcation branches. The drop’s shape is axisymmetric in all cases and we represent the axis of symmetry with an arrow. 2. The bifurcation result Consider the family of bounded domains Ω with boundary ∂Ω deﬁned, in spherical coordinates, by ∂Ω : r = r(θ, ϕ) = R0 + x(θ, ϕ) where x(θ, ϕ) belongs to the set X m+2+α = x ∈ C m+2+α (Σ) , π -periodic in θ, 2π -periodic in ϕ with Σ = [0, 2π] × [0, π] and m ≥ 1.

### Elliptic and Parabolic Problems: A Special Tribute to the Work of Haim Brezis by Andrew Acker (auth.), Catherine Bandle, Henri Berestycki, Bernard Brighi, Alain Brillard, Michel Chipot, Jean-Michel Coron, Carlo Sbordone, Itai Shafrir, Vanda Valente, Giorgio Vergara Caffarelli (eds.)

by Thomas

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