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401-4443-DRL 2 Credits DR D-MATH

Elliptic Partial Differential Equations

Lecturers & Examiners: Prof. Dr. Svitlana Mayboroda
Only for ZGSM (ETH D-MATH and UZH I-MATH) doctoral students. The latter need to register at myStudies and then send an email to with their name, course number and student ID. Please see
VVZ CR n/a

Last Updated: 2026-02-05 16:14:51

Abstract

The course covers fundamental properties of solutions to elliptic partial differential equations and associated boundary value problems, and introduces basic related tools of modern harmonic analysis and geometric measure theory.

Objective

Learn fundamental properties of the elliptic PDEs and associated toolbox of analysis, PDEs, and geometric measure theory.

Content

The course aims to address, in particular, the existence and uniqueness of weak solutions to elliptic equations with bounded measurable coefficients on rough domains, maximum principle and Harnack inequality, interior and boundary regularity (the De Giorgi-Nash-Moser estimates, boundedness and Holder continuity of solutions), comparison principle, the properties of the Green function and harmonic measure, and the relationship between them.

General Information

Language
English
Levels
DR

Examination

Type
ungraded semester performance

Registration & Places

Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
lecture Elliptic Partial Differential Equations
  • Mon 14:15-16:00 (HG G 19.1)
  • 20.11 Date 14:15-16:00 (ML H 37.1)
  • 11.12 Date 14:15-16:00 (ML H 37.1)
2 h weekly
exercise Elliptic Partial Differential Equations
Groups are selected in myStudies. Exercises start in the second week of the semester.
  • Thu 13:15-14:00 (HG E 1.2)
1 h weekly

Offered In