天元讲堂（6.24）Vitaly Moroz
报告题目：Boundary blow-up type solutions to semilinear elliptic equations with
Hardy potential
报告人：Vitaly Moroz（Swansea University, Swansea, UK）
时间：2019年6月24日（星期一）15:30—16:30
地点：苏州大学本部精正楼（数学楼）307
摘要：Semilinear elliptic equations which give rise to boundary blow-up solutions are perturbed by a Hardy potential involving distance to the boundary. The presence of the Hardy potential requires a new definition of large solutions, following the pattern of the associated linear problem. Nonexistence and existence results for different types of solutions will be given. Our considerations are based on a Phragmen-Lindelof type theorem which enables us to classify the solutions and sub-solutions according to their behaviour near the boundary. Nonexistence follows from this principle together with the Keller-Osserman upper bound. The existence proofs rely on sub- and super-solution techniques and on estimates for the Hardy constant.
报告人简介： Vitaly Moroz is a Professor at Mathematics Department, Swansea University. His research is in the Analysis of Nonlinear Partial Differential Equations (PDEs). It is focussed on the fundamental questions of existence, non-existence, and structure of solution sets of nonlinear elliptic equations and inequalities. Recently he was mostly working on nonlinear Schrödinger type equations with nonlocal interactions, such as Choquard-Pekar (Schrödinger-Newton) equations, Schrödinger-Poisson type equations, nonlocal Hartree type equations arising in the density functional theory models for graphene. The common mathematical feature of all these models is that, unlike in the case of classical local PDEs, nonlocal terms are present in the equations via Coulombian type interactions or via a fractional Laplacian term, or both. The tools employed are from the Calculus of Variations, elliptic PDEs theory and Potential Theory. More information of Prof. Moroz can be found at //math.swansea.ac.uk/staff/vm/
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