Strong solution
From Encyclopedia of Mathematics
of a differential equation
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in a domain
A locally integrable function that has locally integrable generalized derivatives of all orders
(cf. Generalized derivative), and satisfies
almost-everywhere in .
The notion of a "strong solution" can also be introduced as follows. A function is called a strong solution of
if there are sequences of smooth (for example, ) functions
,
such that
,
and
for each
, where the convergence is taken in
for any compact set
. In these definitions,
can be replaced by the class
of functions whose
-th powers are locally integrable. The class most often used is
.
In the case of an elliptic equation
both notions of a strong solution coincide.
Comments
References
[a1] | J. Chazarain, A. Piriou, "Introduction à la théorie des équations aux dérivées partielles linéaires" , Gauthier-Villars (1981) pp. 223 MR0598467 Zbl 0446.35001 |
How to Cite This Entry:
Strong solution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Strong_solution&oldid=32910
Strong solution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Strong_solution&oldid=32910
This article was adapted from an original article by A.P. Soldatov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article