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SHARP MORREY regularity theory FOR A FOURTH ORDER GEOMETRICAL EQUATION

Acta Mathematica Scientia 2024年第2期44卷 420-430页

作者：向长林郑高峰 Three Gorges Mathematical Research Center China Three Gorges UniversityYichang443002China School of Mathematics and Statistics Central China Normal UniversityWuhan430079China

This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^regularity theoryu=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey *** work was motivated by many geometrical problems such as the flow of biharmonic *** results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.

关键词： fourth order elliptic equation regularity theory Morrey space decay estimates Riesz potential

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ANISOTROPIC(p,q)-EQUATIONS WITH COMPETITION PHENOMENA

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Acta Mathematica Scientia 2022年第1期42卷 299-322页

作者：刘振海 Nikolaos S.PAPAGEORGIOU Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal UniversityYulin 537000China Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis Guangxi University for NationalitiesNanning 530006China Department of Mathematics National Technical UniversityZografou Campus15780 Athens.Greece

We consider a nonlinear Robin problem driven by the anisotropic(p,q)-Laplacian and with a reaction exhibiting the competing effects of a parametric sublinear(concave) term and of a superlinear(convex) *** prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter *** also prove the existence of a minimal positive solution and determine the monotonicity and continuity properties of the minimal solution map.

关键词： concave-convex nonlinearities anisotropic operators regularity theory maximum principle minimal positive solution

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Finite element methods for fractional diffusion equations

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International Journal of Modeling, Simulation, and Scientific Computing 2020年第4期11卷 32-52页

作者： Yue Zhao Chen Shen Min Qu Weiping Bu Yifa Tang LSEC ICMSECAcademy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190P.R.China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 P.R.China School of Mathematics and Computational Science&Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan 411105P.R.China

Due to the successful applications in engineering,physics,biology,finance,etc.,there has been substantial interest in fractional diffusion equations over the past few decades,and literatures on developing and analyzing efficient and accurate numerical methods for reliably simulating such equations are vast and fast *** paper gives a concise overview on finite element methods for these equations,which are divided into time fractional,space fractional and time-space fractional diffusion ***,we also involve some relevant topics on the regularity theory,the well-posedness,and the fast algorithm.

关键词： Fractional diffusion equation finite element method regularity theory well-posedness fast algorithm.

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