A priori bounds and existence of solutions for some nonlocal elliptic problems

A priori bounds and existence of solutions for some nonlocal elliptic problems
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DOI：
10.4171/rmi/983
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发表时间：
2015-06
期刊：
arXiv: Analysis of PDEs
影响因子：
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通讯作者：
Begoña Barrios;L. D. Pezzo;J. García-Melián;A. Quaas
Begoña Barrios;L. D. Pezzo;J. García-Melián;A. Quaas
中科院分区：
其他
文献类型：
--
作者：
Begoña Barrios;L. D. Pezzo;J. García-Melián;A. Quaas

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本文利用非变分工具证明了一些具有非局部扩散的椭圆型问题解的存在性。我们的证明是基于拓扑度的使用，拓扑度需要了解的先验界。我们采用Gidas和Spruck的经典Scaling方法得到先验界。我们还处理涉及梯度项的问题。
In this paper we show existence of solutions for some elliptic problems with nonlocal diffusion by means of nonvariational tools. Our proof is based on the use of topological degree, which requires a priori bounds for the solutions. We obtain the a priori bounds by adapting the classical scaling method of Gidas and Spruck. We also deal with problems involving gradient terms.