Qualitative Properties of Weak Solutions to Partial Differential Equations - NMMA583

• Title: Kvalitativní vlastnosti slabých řešení parciálních diferenciálních rovnic
• Guaranteed by: Department of Mathematical Analysis (32-KMA)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2014 to 2014
• Semester: winter
• E-Credits: 3
• Hours per week, examination: winter s.:2/0, Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: Czech
• Teaching methods: full-time
• Note: you can enroll for the course repeatedly
• Guarantor: doc. Mgr. Petr Kaplický, Ph.D.; doc. RNDr. Miroslav Bulíček, Ph.D.
• Teacher(s): doc. RNDr. Miroslav Bulíček, Ph.D.; doc. Mgr. Petr Kaplický, Ph.D.
• Class: DS, matematické a počítačové modelování; DS, matematická analýza; M Mgr. MA > Volitelné; M Mgr. MOD > Volitelné; M Mgr. NVM > Volitelné
• Classification: Mathematics > Differential Equations, Potential Theory
• Interchangeability : NDIR247

Annotation

English

This course is devoted to the classical results about regularity and qualitative properties of weak solutions to partial differential equations and their systems. We assume the knowledge of basic theory of weak solutions to partial differential equations.

Last update: T_KMA (14.05.2013)

Czech

Přednáška bude věnovaná klasickým výsledkům o regularitě a dalších kvalitativních vlastnostech slabých řešení parciálních diferenciálních rovnic a jejich systémů. Předpokládáme znalost základů teorie slabých řešení parciálních diferenciálních rovnic.

Last update: T_KMA (14.05.2013)

Aim of the course

English

We intend to pique interest of students in beautiful and difficult branch of mathematics and to learn students some of the classical methods of theory of partial differential equations.

Last update: T_KMA (13.05.2013)

Czech

Vzbudit u studentu zájem o krásnou a nárocnou partii matematiky. Naucit se klasické metody teorie parciálních diferenciálních rovnic.

Last update: T_KMA (13.05.2013)

Literature

[1] Giaquinta, M.: Multiple integrals in the calculus of variations and nonlinear elliptic systems, Annals of Mathematics Studies 105, Princeton University Press, Princeton, NJ, 1983.

[2] L. C. Evans: Partial regularity for stationary harmonic maps into spheres. Arch. Ration. Mech. Anal. *116*(2), 101-113 (1991).

[3] M. Bulíček and J. Frehse: /C^\alpha regularity for a class of non-diagonal elliptic systems with p-growth/ , Calc. Var. Partial Differential Equations, *43*, No. 3, 441--462, 2012

[4] M. Bulíček, J. Frehse and M. Steinhauer: /Everywhere C^\alpha -estimates for a class of nonlinear elliptic systems with critical growth/, Adv. Calc.Var, online first, 2013

Last update: T_KMA (14.05.2013)

Syllabus

This course is devoted to the new results about regularity of minimizers to variational integrals. We discuss results about partial regularity for general class of problems and for integrlas with power-growth and satisfying the so-called splitting condition we show that any minimizer is a Holder continuous mapping.

Last update: Kaplický Petr, doc. Mgr., Ph.D. (05.10.2016)