Beskjeder

Exercise set 3 can be downloaded from

http://folk.uio.no/siddharm/assignment3.pdf

Syllabus for the Exam,

Sobolev spaces: Definitions, Approximations, Traces, Gagliardo-Nirenberg-Sobolev inequality, Morrey's inequality, Compactness

Linear Elliptic PDEs: Weak solutions, Existence and uniqueness by Riesz Representation theorem and Lax-Milgram Lemma, Regularity of solutions to linear Elliptic PDEs. All the best for the exam

A set of problems dealing with Sobolev spaces can be downloaded from folk.uio.no/siddharm/assignment2.pdf

This is NOT a obligatory exercise set. However, solving the problems will be very beneficial for the examination. I encourage you to submit answersheets to me.

The corrected obligatory exercise set 1 can be collected from the Math office. No class on wednesday 5th november.

First obligatory assignment can be downloaded from

folk.uio.no/siddharm/assignment1.pdf

The due date is 24th October

In the last couple of lectures, i have described explicit solutions of the Poisson's equations in multi-space dimensions in detail. We started with construction of fundamental solutions and proof of the Poisson's formula.

We have also obtained representation formula in terms of Green's function for the Boundary value problem. The material is in chapter 2, 2.2.1 and 2.2.4.

In the next lecture, we will continue to study the Green's function representation.

Wednesday lecture is in room no B1036.

Today, i considered a general elliptic equation in one d and derived estimates on the solution in terms of Sobolev norms.

On 18th, i started with a general description of PDEs and this course. I considered the Poisson's equation in one dimension and derived an explicit formula in terms of Green's function. Estimates on the solutions and the derivatives in terms of integrals were also derived.

There is no lecture on wednesday, 20th