Hörmander's Condition

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, Hörmander''s condition is a property of vector fields that, if satisfied, has many useful consequences in the theory of partial and stochastic differential equations. The condition is named after the Swedish mathematician Lars Hörmander. In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a subset of Euclidean space. Vector fields are often used in physics to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from point to point.