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Course, academic year 2019/2020
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Qualitative properties of weak solutions to partial differential equations - NDIR247
Title in English: Kvalitativní vlastnosti slabých řešení parciálních diferenciálních rovnic
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2013
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not taught
Language: Czech
Teaching methods: full-time
Note: you can enroll for the course repeatedly
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Interchangeability : NMNV567
Annotation -
Last update: G_M (24.05.2010)
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, e.g. course NDIR045.
Aim of the course -
Last update: G_M (24.05.2010)

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.

Literature -
Last update: doc. Mgr. Petr Kaplický, Ph.D. (07.09.2012)

[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. Diening, P. Kaplický, S. Schwarzacher: BMO estimates for the p-Laplacian, Nonlinear Analysis 75, 637-650, 2012.

[3] L. Diening, P. Kaplický: Lq theory for a generalized Stokes system, Manuscripta Mathematica, 2012.

[4] L. Diening, P. Kaplický, S. Schwarzacher: BMO estimates for the generalized Stokes system in 2D, 2012.

[5] L. Diening, F. Ettwein: Fractional estimates for non-differentiable elliptic systems with general growth. Forum Math. 20, no. 3, 523-556, 2008.

Syllabus -
Last update: doc. Mgr. Petr Kaplický, Ph.D. (07.09.2012)

In the academic year 2012-2013 we concentrate on studies of optimal regularity in Campanato spaces of weak solutions to elliptic linear and nonlinear equations and systems. We will also consider the problems where the growth of the elliptic term is given by some N-function.

 
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