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analysis tools (Sobolev spaces, singular integrals) and to explain how these tools are Louis Nirenberg, On elliptic partial differential equations, Ann. Sc. Norm. Sup. . A continuous function u defines a distribution, still denoted u, through the .
Table of contents

Supplementary Information

The course consists of three parts. The first part divided in two chapters develops further tools needed for the study of boundary value problem, namely distributions and Sobolev spaces.

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The following two parts are devoted to elliptic and parabolic equations on bounded domains. They present the variational approach and spectral theory of elliptic operators as well as their use in the existence theory for parabolic problems. Extra reading about elliptic equations on the whole space case will be given.

The aim of the course is to expose the students some important aspects of Partial Differential Equation theory, aspects that will be most useful to those who will further work with Partial Differential Equations be it on the Theoretical side or on the Numerical one.

Debnath and P. Introduction to Hilbert Spaces with Applications Press,.

Ebook Distributions Sobolev Spaces Elliptic Equations

Third edition. Demengel and G.

11 Adimurthi - Basics of functional analysis, Sobolev spaces

Analysis tools with applications. Global Analysis on Open Manifolds. Nova Science Publishers. Partial Differential Equations. American Mathematical Society,.

Fundamentals of Applied Functional Analysis

Higher covariant derivatives. Grosse and C. Sobolev spaces on Riemannian manifolds with bounded geometry: general coordinates and traces. Grosser, M. Kunzinger, M. Oberguggenberger, and R.


Sobolev spaces on Riemannian manifolds, volume of Lecture notes in mathematics Berlin, New York. American Mathematical Society. Inci, T.

Kappeler, and P. On the Regularity of the Composition of Diffeomorphisms, volume Memoirs of the American Mathematical Society. John Douglas Moore. Lectures on differential geometry. Riemannian Manifolds: An Introduction to Curvature.

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Introduction to smooth manifolds. Introduction to Smooth Manifolds Second edition. Nezza, G. Palatucci, and E. Bulletin des Sciences Mathmatiques, 5 Seminar on the Atiyah-Singer Index Theorem.

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    An introduction to functional spaces.