Maximum principles for elliptic systems of partial differential equations

• Thesis title in Czech: Principy maxima pro nelineární systémy eliptických parciálních diferenciálních rovnic
• Thesis title in English: Maximum principles for elliptic systems of partial differential equations
• Key words: princip maxima, eliptické systémy, Bellmanovy systémy, teorie her
• English key words: maximum principle, elliptic systems, Bellman systems, game theory
• Academic year of topic announcement: 2016/2017
• Thesis type: diploma thesis
• Thesis language: angličtina
• Department: Mathematical Institute of Charles University (32-MUUK)
• Supervisor: doc. RNDr. Miroslav Bulíček, Ph.D.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 16.05.2016
• Date of assignment: 16.05.2016
• Confirmed by Study dept. on: 31.05.2016
• Date and time of defence: 15.09.2017 00:00
• Date of electronic submission: 21.07.2017
• Date of submission of printed version: 21.07.2017
• Date of proceeded defence: 15.09.2017
• Opponents: doc. Mgr. Petr Kaplický, Ph.D.

Guidelines

Student by se měl seznaámit se základy matematické teorie pro Bellmanovy systémy. Potom by se měl pokusit navrhnout vhodnout strukturu tzv. Lagrangiánů tak, aby výsledný systém eliptických rovnic stále splňoval princip maxima/minima.

References

M. Bulíček and J. Frehse: On nonlinear elliptic Bellman systems for a class of stochastic differential games in arbitrary dimension, Math. Models Methods Appl. Sci., 21, No. 1, 215--240, 2011

L. Beck, M. Bulíček and J. Frehse: Old and new results in regularity theory for diagonal elliptic systems via blow up techniques, J. Differential Equations, 259, No. 11, 6528--6572, 2015