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Inequalities In Rearrangement Invariant Function Spaces
, 1995
"... Introduction. Set up by Hardy & Littlewood, a theory of rearrangements was popularized by the wellknown book [HLP]. Rearrangements of functions are frequently used in real and harmonic analysis, in investigations about singular integrals and function spaces  see, e.g., [He], [ON], [ONW], [SW ..."
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Cited by 43 (2 self)
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Introduction. Set up by Hardy & Littlewood, a theory of rearrangements was popularized by the wellknown book [HLP]. Rearrangements of functions are frequently used in real and harmonic analysis, in investigations about singular integrals and function spaces  see, e.g., [He], [ON], [ONW], [SW]. P'olya & Szego and their followers demonstrated a good many isoperimetric theorems and inequalities by means of rearrangements  see [PS], a source book on this matter. More recent investigations have shown 178 G. TALENTI that rearrangements of functions fit well also into the theory of elliptic secondorder partial differential equations  see, e.g., [Bae], [Ta3] and the bibliography therein. Several types of rearrangements are known  presentations are in [Ka] and [Bae]. Here we limit ourselves to rearrangements `a la Hardy & Littlewood. 1.2. Definitions and basic properties. Let G be a measurable subset of R<F
Rearrangements of vector valued functions, with application to atmospheric and oceanic ows
"... This paper establishes the equivalence of four de nitions of two vector valued functions being rearrangements, and gives a characterisation of the set of rearrangements of a prescribed function. The theory of monotone rearrangement ofavector valued function is used to show the existence and uniquene ..."
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This paper establishes the equivalence of four de nitions of two vector valued functions being rearrangements, and gives a characterisation of the set of rearrangements of a prescribed function. The theory of monotone rearrangement ofavector valued function is used to show the existence and uniqueness of the minimiser of an energy functional arising from a model for atmospheric and oceanic ow. At each xed time solutions are shown to be equal to the gradient of a convex function, verifying the conjecture of Cullen, Norbury and Purser. Key words Rearrangement of functions, semigeostrophic, variational problems, generalised solution.
Multiconstrained Variational Problems in Magnetohydrodynamics, I: Equilibrium
"... Introduction 2 Variational formulation In this section we pose the variational problem whose solutions represent axisymmetric equilibrium configurations of a plasma confined in a tokomak or some other toroidal device. The geometry of the configurations we consider is depicted schematically in Figur ..."
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Introduction 2 Variational formulation In this section we pose the variational problem whose solutions represent axisymmetric equilibrium configurations of a plasma confined in a tokomak or some other toroidal device. The geometry of the configurations we consider is depicted schematically in Figure 1. In the usual cylindrical coordinates the toroidal region D = fx = (r; OE; z) 2 R 3 : (r; z) 2\Omega ; 0 OE ! 2g is determined by its crosssection \Omega\Gamma a domain in the halfplane R 2 + = f(r; z) : r ? 0g. In D the plasmavacuum system is governed by the ideal magnetohydrodynamic equilibrium equations J \Theta B = rp; r \Theta B =<F1
Multiconstrained Variational Problems in Magnetohydrodynamics, II: Slow Evolution
"... Introduction 2 Slow evolution equations We begin by recalling the full set of equations governing a plasmavacuum system confined in a toroidal device such as a tokomak. Under the usual assumptions of ideal magnetohydrodynamics, the equations valid in the plasma region are Dae Dt + aer \Delta V = ..."
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Introduction 2 Slow evolution equations We begin by recalling the full set of equations governing a plasmavacuum system confined in a toroidal device such as a tokomak. Under the usual assumptions of ideal magnetohydrodynamics, the equations valid in the plasma region are Dae Dt + aer \Delta V = q M (2.1) Di Dt + ir \Delta V = q S (2.2) ae DV Dt +rp \Gamma J \Theta B = Q (2.3) @B @t \Gamma r \Theta (V \Theta B) = 0 (2.4) r \Theta B = J; r \Delta B = 0 ; (2.5) and the equations valid in the vacuum region are r \Theta B = J; r \Delta B = 0 :
JOURNAL OF COMPUTATIONAL AND
, 1992
"... Numerical algorithm for the calculation of nonsymmetric dipolar and rotating monopolar vortex structures B.W. van de Fliert*, E. van Groesen, R. de Roo, R.W. de Vries ..."
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Numerical algorithm for the calculation of nonsymmetric dipolar and rotating monopolar vortex structures B.W. van de Fliert*, E. van Groesen, R. de Roo, R.W. de Vries