A note on estimates of the Newtonian potential on bounded domains
Tran Vu Khanh, Andrew Raich · Mathematical Inequalities & Applications · 2024
In this paper, we investigate the regularity of the operator K on a smooth bounded domain in R d given by convolution against the Newtonian potential.We show that the gain in L p -Sobolev spaces agrees with elliptic regularity.We also establish L p -Sobolev to L q -Sobolev bounds as well as bounds from L -Sobolev spaces to Hölder spaces.