Isolated singularities of polyharmonic inequalities [chapter]

Marius Ghergu, Steven D. Taliaferro
Isolated Singularities in Partial Differential Inequalities  
We study nonnegative classical solutions u of the polyharmonic inequality We give necessary and sufficient conditions on integers n ≥ 2 and m ≥ 1 such that these solutions u satisfy a pointwise a priori bound as x → 0. In this case we show that the optimal bound for u is where Γ is the fundamental solution of −∆ in R n .
doi:10.1017/cbo9781316481363.007 fatcat:ub7cyu6tojha5pldbkn6rrwfy4