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ON A CLASS OF SOBOLEV FUNCTIONS AND ITS APPLICATIONS TO HIGHER-ORDER ELLIPTIC EQUATIONS

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  01 June 2008

MAMADOU SANGO
MAMADOU SANGO*
Affiliation:
IHES, Le Bois-Marie, Rue de Chartres, F-91440 Bures-sur-Yvettes, France Current address: Department of Mathematics and Applied Mathematics, University of Pretoria, Mamelodi Campus, 0002, Pretoria, South Africa (email: mamadou.sango@up.ac.za)
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Abstract

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It is well known that higher-order linear elliptic equations with measurable coefficients and higher-order nonlinear elliptic equations with analytic coefficients can admit unbounded solutions, unlike their second-order counterparts. In this work we introduce the concept of approximate truncates for functions in higher-order Sobolev spaces and prove that if a solution of a higher-order linear elliptic equation has an approximate truncate somewhere then it is bounded there.

Keywords

Sobolev spaceshigher-order elliptic equationsapproximate truncates

MSC classification

Secondary: 35J30: Higher-order elliptic equations 35J35: Variational methods for higher-order elliptic equations 35J40: Boundary value problems for higher-order elliptic equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 3 , June 2008 , pp. 405 - 417
Copyright
Copyright © 2008 Australian Mathematical Society

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