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 | A second order linear partial differential equation can be written as | ||
<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>. | <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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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> given. | ||
| − | + | </p> | |
Revision as of 15:23, 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
.
If 
is positive or negative definite, the partial differential equation is called elliptic.
An example is the Poisson's equation: 
,
where 
denotes the Laplace operator, 
is the unknown, and the function 
given.
Pages in category "Elliptic"
The following 2 pages are in this category, out of 2 total.
