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. | ||
| + | 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>. | ||
| + | |||
| + | If <math>A=(a_{i,j})_{i,j}</math> is positive or negative definite, the partial differential equation is called elliptic. | ||
| + | |||
| + | 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. | ||
| + | |||
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
. 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.
