Nonlinear systems of elliptic equations with natural growth conditions and sign conditions

Alain Bensoussan; Lucio Boccardo

doi:10.1007/s00245-002-0753-3

Author(s)

Alain Bensoussan
Lucio Boccardo

Detail(s)

Original language	English
Pages (from-to)	143-166
Journal / Publication	Applied Mathematics and Optimization
Volume	46
Issue number	2-3
Publication status	Published - Sept 2002
Externally published	Yes

Link(s)

DOI	DOI https://doi.org/10.1007/s00245-002-0753-3 Final Published version
	Check@CityULib
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-0142007891&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(4451300f-2302-4e54-80aa-e5391e37ed67).html

Abstract

In the theory of nonlinear systems of partial differential equations, with a nonlinear term depending on the gradient having natural growth, which means, for instance, a quadratic growth for a function expected to be in H¹, it is essential to look for solutions which are bounded. However, there are natural cases in which bounded solutions are out of reach. This paper revisits previous works in this subject, with some improvement in the proofs, and some extension of the results. The case of systems which will naturally include the case of a single equation is considered. An alternative proof which does not seem to carry over to systems is also proposed.

Citation Format(s)

[ RIS ] [ BibTeX ]

Nonlinear systems of elliptic equations with natural growth conditions and sign conditions. / Bensoussan, Alain; Boccardo, Lucio.
In: Applied Mathematics and Optimization, Vol. 46, No. 2-3, 09.2002, p. 143-166.

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Bensoussan, A & Boccardo, L 2002, 'Nonlinear systems of elliptic equations with natural growth conditions and sign conditions', Applied Mathematics and Optimization, vol. 46, no. 2-3, pp. 143-166. https://doi.org/10.1007/s00245-002-0753-3

Bensoussan, A., & Boccardo, L. (2002). Nonlinear systems of elliptic equations with natural growth conditions and sign conditions. Applied Mathematics and Optimization, 46(2-3), 143-166. https://doi.org/10.1007/s00245-002-0753-3

Bensoussan A, Boccardo L. Nonlinear systems of elliptic equations with natural growth conditions and sign conditions. Applied Mathematics and Optimization. 2002 Sept;46(2-3):143-166. doi: 10.1007/s00245-002-0753-3

Bensoussan, Alain ; Boccardo, Lucio. / Nonlinear systems of elliptic equations with natural growth conditions and sign conditions. In: Applied Mathematics and Optimization. 2002 ; Vol. 46, No. 2-3. pp. 143-166.