Difference between revisions of "Category:Elliptic"

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This category contains all control problems which are governed by an elliptic partial differential equation.
 
This category contains all control problems which are governed by an elliptic partial differential equation.
  
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A second order linear partial differential equation can be written as
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<math>\sum^n_{i,j=1} a_{i,j} \frac{\partial^2}{\partial x_i \partial x_j} +\quad \textrm{ lower-order terms} = 0</math>.
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If <math>A=(a_{i,j})_{i,j}</math> is positive or negative definite, the partial differential equation is called elliptic.
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An example is the Poisson's equation: <math>-\Delta u = f</math>,
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where <math>\Delta</math> denotes the Laplace operator, <math>u</math> is the unknown, and the function <math>f</math> given.
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Revision as of 15:22, 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_{i,j} \frac{\partial^2}{\partial x_i \partial x_j} +\quad \textrm{ lower-order terms} = 0.

If A=(a_{i,j})_{i,j} 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 given.

Pages in category "Elliptic"

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