Nonlinear equations with negative exponents

来源 :2016年非线性偏微分方程和变分方法及其应用研讨会(Workshop on Nonlinear PDEs and Cal | 被引量 : 0次 | 上传用户：leinuo2222

【摘要】

：

　　Let Ω(() RN be a bounded regular domain of dimension N ≥ 1, h a positive L1 function on Ω. Elliptic equations of singular growth like -△u = h(x)/ up in

【作者】

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Yijing Sun

【机构】

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UniversityofChineseAcademyofSciences,China

【出处】

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2016年非线性偏微分方程和变分方法及其应用研讨会(Workshop on Nonlinear PDEs and Cal

【发表日期】

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2016年5期

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　　Let Ω(() RN be a bounded regular domain of dimension N ≥ 1, h a positive L1 function on Ω. Elliptic equations of singular growth like -△u = h(x)/ up in Ω; u > 0 in Ω; u = 0 on (e)Ω have been the target of investigation for decades. A very nice result for existence of solutions of such an equation is due to Lazer-McKenna [Proc.AMS 111(1991)720-730] when h is a positive continuous function on (Ω). In that paper the Lazer-McKenna obstruction was first presented: the equation has a H10 -solution if and only if p < 3. In this talk we derive a compatible condition between coefficients and negative exponents which is optimal for H1 0 -solutions of strongly singular problems and reveal the role of -3 for elliptic equations with negative exponents. We shall also introduce some about Lp Minkowski problem for all p < 0.

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