Annales Academię Scientiarum Fennicę
Mathematica
Volumen 33, 2008, 171-204

SUPERHARMONIC FUNCTIONS AND DIFFERENTIAL EQUATIONS INVOLVING MEASURES FOR QUASILINEAR ELLIPTIC OPERATORS WITH LOWER ORDER TERMS

Takayori Ono

Fukuyama University
Gakuencho, Fukuyama, 729-0292 Japan; ono 'at' fuhc.fukuyama-u.ac.jp

Abstract. We consider superharmonic functions relative to a quasi-linear second order elliptic differential operator L with lower order term and weighted structure conditions. We show that, given a nonnegative finite Radon measure \nu, there is a superharmonic function u satisfying Lu = \nu with weak zero boundary values. Moreover, we give a pointwise upper estimate for superharmonic functions in terms of the Wolff potential.

2000 Mathematics Subject Classification: Primary 31C45; Secondary 31B05, 35J60.

Key words: (A,B)-superharmonic function, quasi-linear equation, involving measure, Wolff potential.

Reference to this article: T. Ono: Superharmonic functions and differential equations involving measures for quasilinear elliptic operators with lower order terms. Ann. Acad. Sci. Fenn. Math. 33 (2008), 171-204.

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