MS-E1210 - Sobolev Spaces D, Project, 1.8.2024-31.7.2025

Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.

LEARNING OUTCOMES

After this course a student will know Sobolev space techinques in oder to be able to apply them in partial differential equations.

Credits: 5 - 10

Schedule: 01.08.2024 - 31.07.2025

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Juha Kinnunen

Contact information for the course (applies in this implementation):

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English

CONTENT, ASSESSMENT AND WORKLOAD

Content

  • valid for whole curriculum period:

    Definition and properties of weak derivatives, approximation by smooth functions, properties and characterizations of Sobolev spaces, Sobolev inequalities, Sobolev capacity, Lebesgue points for Sobolev functions, Sobolev spaces with zero boundary values, harmonic analysis methods for Sobolev spaces. Additional material is discussed case by case.

Assessment Methods and Criteria

  • valid for whole curriculum period:

    Homework assignments and attendance (100%).

     

Workload

  • valid for whole curriculum period:

    There are no regular lectures in the course. Study methods: self-study and homework assingments (at least 100 h), meetings with a group or a teaching assistant (24 h), meetings with the instructor (12 h).

DETAILS

Study Material

  • valid for whole curriculum period:

    The lecture notes and homework assignments are available on the course homepage.

Substitutes for Courses
Prerequisites
SDG: Sustainable Development Goals

    4 Quality Education

FURTHER INFORMATION

Further Information

  • valid for whole curriculum period:

    Teaching Language: English

    Teaching Period: 2024-2025 Autumn I - Spring V
    2025-2026 Autumn I - Spring V

    Registration:

    Registration takes place in Sisu (sisu.aalto.fi). Participants are asked to contact the responsible teacher before registering. The course can be taken individually or as a group. The course can be started anytime and the schedule is discussed case by case. 

Rules of Conduct - Students´ Rights and Responsibilities (in force from 1 August 2020)

Aalto University Code of Academic Integrity and Handling Violations Thereof