Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 35, 2010, 633-640

A POTENTIAL THEORY APPROACH TO THE EQUATION -\Delta u = |\nabla u|²

Anna Tuhola-Kujanpää

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland; anna.tuhola-kujanpaa 'at' jyu.fi

Abstract. In this paper we show that if

-\Delta u = |\nabla u|² in \Omega,
-\Delta u \in W₀^1,2(\Omega),

then

-\Delta (e^u - 1) = \mu in \Omega,

when \mu \perp cap₂, and conversely.

2000 Mathematics Subject Classification: Primary 35J05, 35J25, 31B20, 31B05.

Key words: Elliptic equations, singular solutions, uniqueness.

Reference to this article: A. Tuhola-Kujanpää: A potential theory approach to the equation -\Delta u = |\nabla u|². Ann. Acad. Sci. Fenn. Math. 35 (2010), 633-640.

Full document as PDF file

doi:10.5186/aasfm.2010.3540

A POTENTIAL THEORY APPROACH TO THE EQUATION -\Delta u = |\nabla u|2

Anna Tuhola-Kujanpää

A POTENTIAL THEORY APPROACH TO THE EQUATION -\Delta u = |\nabla u|²