Differential and Integral Equations

Galerkin approximation, strong continuity of the relative rearrangement map and application to plasma physics equations

J.-M. Rakotoson

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Abstract

We prove a strong continuity result for the relative rearrangement map. This new result and its corollary are used for the resolution of equations of the form $-\Delta u = F(u)$ via a Brouwer fixed point theorem. The nonlocal nonlinearity $F$ might depend on the monotone rearrangement $u_*$, its derivative $u'_*$ and the relative rearrangement of $u$ with respect to the data.

Article information

Source
Differential Integral Equations, Volume 12, Number 1 (1999), 67-81.

Dates
First available in Project Euclid: 29 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367266994

Mathematical Reviews number (MathSciNet)
MR1668537

Zentralblatt MATH identifier
1005.76097

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 47N20: Applications to differential and integral equations 76X05: Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10]

Citation

Rakotoson, J.-M. Galerkin approximation, strong continuity of the relative rearrangement map and application to plasma physics equations. Differential Integral Equations 12 (1999), no. 1, 67--81. https://projecteuclid.org/euclid.die/1367266994


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