It is known that [here] the following PDE
has no solution. However, this is no longer true if we replace the whole space by a ball of radius
, say
. In this entry, we show that if
is a solution of
then
.
To this purpose, let us recall the following
The Maximum Principle. Let assume be open and bounded. We consider an elliptic operator
of the form
where coefficients are continuous and the standard uniform ellipticity condition holds.