In the one-dimensional situation the p -superharmonic functions are exactly the concave functions and in several dimensions, the concave functions are p- superharmonic, simultaneously for all p, but there are p-superharmonic functions that it aren't concave. How can we see this?

Jadon Camacho

Jadon Camacho

Answered question

2022-11-11

In the one-dimensional situation the p -superharmonic functions are exactly the concave functions and in several dimensions, the concave functions are p-superharmonic, simultaneously for all p, but there are p-superharmonic functions that it aren't concave. How can we see this?

Answer & Explanation

jennasyliang4tr

jennasyliang4tr

Beginner2022-11-12Added 15 answers

Ley f ( x , y ) = x 2 y 2 . Then f is a 2-harmonic function. It is not concave, nor convex.
Every p-harmonic function is p-subharmonic and p-superharmonic.

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