# 101.785 AKANA Regularity of solutions to elliptic equations This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_20",{id:"j_id_20",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_22",{id:"j_id_22",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2019S

2019S, SV, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: SV Special Lecture

## Aim of course

The lecture offers students an insight into selected techniques for the regularity of solutions to second-order elliptic equations. In the lecture students learn to analyze the fundamental solution, to apply Caccioppoli estimates and to work with Morrey and Campanato spaces. Furthermore, the Moser-iteration is covered by this lecture. The goal is the development of a toolbox of techniques for the regularity of solutions of elliptical equations.

## Subject of course

Elliptical equations occur in various applications in physics, chemistry and biology. Examples are equations from electrostatics and gravitation. Furthermore, elliptical equations can be found as stationary problems describing the diffusion of a chemical in a solution. If one wants to calculate the solutions numerically in these cases, it turns out that the numerical methods usually converge faster the more regular the solution of the elliptical equation is. On the one hand, direct methods using the fundamental solution are treated. On the other hand, the H^m regularity and the Hölderegularity of solutions of elliptic equations are also proved.

## Lecturers

• Braukhoff, Marcel Hendrik

## Course dates

DayTimeDateLocationDescription
Thu14:00 - 16:0007.03.2019 - 27.06.2019 DAgrün03CDr. Braukhoff
AKANA Regularity of solutions to elliptic equations - Single appointments
DayDateTimeLocationDescription
Thu07.03.201914:00 - 16:00 DAgrün03CDr. Braukhoff
Thu14.03.201914:00 - 16:00 DAgrün03CDr. Braukhoff
Thu21.03.201914:00 - 16:00 DAgrün03CDr. Braukhoff
Thu28.03.201914:00 - 16:00 DAgrün03CDr. Braukhoff
Thu04.04.201914:00 - 16:00 DAgrün03CDr. Braukhoff
Thu11.04.201914:00 - 16:00 DAgrün03CDr. Braukhoff
Thu18.04.201914:00 - 16:00 DAgrün03CDr. Braukhoff
Thu25.04.201914:00 - 16:00 DAgrün03CDr. Braukhoff
Thu02.05.201914:00 - 16:00 DAgrün03CDr. Braukhoff
Thu09.05.201914:00 - 16:00 DAgrün03CDr. Braukhoff
Thu16.05.201914:00 - 16:00 DAgrün03CDr. Braukhoff
Thu23.05.201914:00 - 16:00 DAgrün03CDr. Braukhoff
Thu06.06.201914:00 - 16:00 DAgrün03CDr. Braukhoff
Thu13.06.201914:00 - 16:00 DAgrün03CDr. Braukhoff
Thu27.06.201914:00 - 16:00 DAgrün03CDr. Braukhoff

Not necessary

## Literature

Partial Differential Equations (Graduate Studies in Mathematics, Band 19) of Lawrence C. Evans (2010)
An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs vof Mariano Giaquinta and Luca Martinazzi
Elliptic Partial Differential Equations of Second Order of David Gilbarg and  Neil S. Trudinger (1977)

German