论文标题
一个非本地耦合模型，涉及三个分数laplacians
A non-local coupling model involving three fractional laplacians
论文作者
论文摘要
在本文中，我们研究了一个非本地扩散问题，涉及在两个领域作用的三个不同的拉普拉斯算子。每个域都有一个关联的操作员来控制其扩散，第三个操作员用作两个操作机构之间的耦合机制。提出的模型是非本地能量功能的梯度流。在本文的第一部分中，我们提供了有关解决方案的存在和质量保护的结果。第二部分包含有关溶液的LP衰变的结果。当两个域是一个球及其互补的时，第三部分致力于研究问题解决方案的渐近行为。附录还提供了外部分数Sobolev和NASH独立利益的不平等现象。
In this article we study a non-local diffusion problem that involves three different fractional Laplacian operators acting on two domains. Each domain has an associated operator that governs the diffusion on it, and the third operator serves as a coupling mechanism between the two of them. The model proposed is the gradient flow of a non-local energy functional. In the first part of the article we provide results about existence of solutions and the conservation of mass. The second part encompasses results about the Lp decay of the solutions. The third part is devoted to study the asymptotic behavior of the solutions of the problem when the two domains are a ball and its complementary. Exterior fractional Sobolev and Nash inequalities of independent interest are also provided in an appendix.
