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Information about the class of compactly supported smooth functions $u$ on $Ω\subset R^n$ such that $Δu≥0?$ Do a significant class of such function exist?

NB. This type of function may be useful in the problems of controllability.

In the case $n=1$, we can construct geometrically some functions with the above mentioned conditions.

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Look up superharmonic and subharmonic functions.

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