-bounds for general singular elliptic equations with convection term
Section snippets
Introduction and assumptions
Let be a bounded domain with a Lipschitz boundary . In this paper, we are concerned with the following problem where we assume the subsequent hypotheses:
- (H)
The functions and are supposed to be Carathéodory functions such that for all , for all , with nonnegative constants
Proof of the main result
Before we give the proof of Theorem 1.1 we begin with a truncation lemma which was motivated by the work of Giacomoni–Schindler–Takáč [1].
Let .
Lemma 2.1 Let the hypotheses (H) be satisfied and let be a weak solution of problem (1.1). Then, for all nonnegative functions and for some .
Proof Let be a weak solution of (1.1). We take a -cut-off function such that
Acknowledgments
The authors thank the referees for their valuable comments.
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