József Lőrinczi

I will consider a class of non-local equations, assuming that their solutions have a global maximum, and discuss estimates on their position. Such points are of special interest as they describe where hot-spots settle on the long run or, in a probabilistic description, the region around which paths typically concentrate. I will address, on the one hand, the interplay of competing parameters whose compromise the resulting location is, and the impact of geometric constraints, on the other.

References
[1] A. Biswas and J. Lőrinczi. Universal constraints on the location of extrema of eigenfunctions of non-local Schrödinger operators, arXiv:1710.11596, 2017 (under review)
[2] A. Biswas and J. Lőrinczi. Maximum principles and Aleksandrov-Bakelman-Pucci type estimates for non-local Schrödinger equations with exterior conditions, arXiv:1711.09267, 2017 (under review)
[3] A. Biswas and J. Lőrinczi. Maximum principles for time-fractional Cauchy problems with spatially non-local components, arXiv:1801.02349, 2018 (under review)
[4] A. Biswas and J. Lőrinczi. Ambrosetti-Prodi type results for Dirichlet problems of the fractional Laplacian, arXiv:1803.08540, 2018 (under review)