Difference between revisions of "Category:Elliptic"

From mintOC
Jump to: navigation, search
Line 7: Line 7:
 
   
 
   
 
  An example is the Poisson's equation: <math>-\Delta u = f</math>,
 
  An example is the Poisson's equation: <math>-\Delta u = f</math>,
  where <math>\Delta</math> denotes the Laplace operator, <math>u</math> is the unknown, and the function <math>f</math> given.
+
  where <math>\Delta</math> denotes the Laplace operator, <math>u</math> is the unknown, and the function <math>f</math> is given.
 
  </p>
 
  </p>
  

Revision as of 15:33, 24 February 2016

This category contains all control problems which are governed by an elliptic partial differential equation.

A second order linear partial differential equation can be written as \sum^n_{i,j=1} a_{ij} \frac{\partial^2 u}{\partial x_i \partial x_j} +\quad \textrm{ lower-order terms} = 0. If A=(a_{ij})_{ij} is positive or negative definite, the partial differential equation is called elliptic. An example is the Poisson's equation: -\Delta u = f, where \Delta denotes the Laplace operator, u is the unknown, and the function f is given.

Pages in category "Elliptic"

The following 2 pages are in this category, out of 2 total.