Lecture

General Second Order Elliptic Equations

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

MATH-305: Introduction to partial differential equations

This is an introductory course on Elliptic Partial Differential Equations. The course will cover the theory of both classical and generalized (weak) solutions of elliptic PDEs. ...

Description

This lecture covers the topic of general second-order elliptic equations, including weak solutions, uniqueness of solutions, a priori bounds, and the strong maximum principle. The lecture also discusses the notation and properties of linear elliptic equations, providing technical results from linear algebra to support the theoretical concepts.

Instructors (2)

Fabio Nobile

Teaching & PhD PhD Students Veronica Montanaro, Matteo Raviola, Francesca Bettinelli, Eliott Van Dieren, Riccardo Saporiti, Giacomo Mossinelli, Noé Stauffer, Fabio Zoccolan Past EPFL PhD Students Diane Sylvie Guignard, Francesco Tesei, Eleonora Musharbash, Matthieu Claude Martin, Davide Pradovera, Sundar Subramaniam Ganesh, Eva Vidlicková, Juan Pablo Madrigal Cianci, Andrea Zanoni, Thomas Simon Spencer Trigo Trindade Past EPFL PhD Students as codirector Michele Pisaroni Courses Advanced analysis II - ve

Nicola De Nitti

Official source

Related concepts (32)

Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.

Buffer solution

A buffer solution (more precisely, pH buffer or hydrogen ion buffer) is an acid or a base aqueous solution consisting of a mixture of a weak acid and its conjugate base, or vice versa. Its pH changes very little when a small amount of strong acid or base is added to it. Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of chemical applications. In nature, there are many living systems that use buffering for pH regulation.

Aqueous solution

An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be represented as . The word aqueous (which comes from aqua) means pertaining to, related to, similar to, or dissolved in, water. As water is an excellent solvent and is also naturally abundant, it is a ubiquitous solvent in chemistry.

Acid strength

Acid strength is the tendency of an acid, symbolised by the chemical formula HA, to dissociate into a proton, H+, and an anion, A-. The dissociation of a strong acid in solution is effectively complete, except in its most concentrated solutions. HA -> H+ + A- Examples of strong acids are hydrochloric acid (HCl), perchloric acid (HClO4), nitric acid (HNO3) and sulfuric acid (H2SO4). A weak acid is only partially dissociated, with both the undissociated acid and its dissociation products being present, in solution, in equilibrium with each other.

Linear map

In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .

Related lectures (64)

Classification of PDEs: Linear, Semi-linear, Quasi-linear

Explores the classification of PDEs into linear, semi-linear, and quasi-linear types, emphasizing the properties of their solutions.

Linear Algebra: Matrix Operations and Basis

Explores matrix operations, rank determination, kernel dimensions, and basis concepts in linear algebra.

Linear PDEs of Order 2

Covers linear PDEs of order 2, focusing on elliptic second-order PDEs and boundary conditions.

Linear Algebra Basics

Covers the basics of linear algebra, including solving equations and understanding systems of linear equations graphically.

Weak Formulations & Solutions: Elliptic Problems