On the Potential Theory of the KOLMOGOROV Equation

✍ Scribed by Walter Hoh; Niels Jacob

• Publisher: John Wiley and Sons
• Year: 1991
• Tongue: English
• Weight: 634 KB
• Volume: 154
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19911540106

✦ Synopsis

We prove a mean value theorem for the solutions of the backward KOLMOGOROV equation. The mean values are taken over the level surfaces of the fundamental solution of the formally adjoint operator with respect to a certain measure which is identified with a measure obtained by a sweeping out procedure in the harmonic space generated by the KOLMWROV operator. Further we prove that the harmonic space under consideration is a strongly harmonic space and that single points are polar in this space. This makes it possible to apply a recent result of H. BAUER on the fine boundary behaviour of generalized harmonic functions.