R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Maximum Principles for the Schroedinger Operator with Singular Potential
Augusto Ponce (Universite Catholique de Louvain, Belgium)
Abstract:
The Schroedinger operator
in
has been extensively studied for potentials in
and even
with any exponent
.
Kato's inequality published in the Israel J. Math. in the 1970s was a major breakthrough in spectral problems by allowing one to consider potentials
that are merely
, and a few years later Ancona proved a version of the strong maximum principle up to sets of zero Newtonian capacity.
We present new counterparts of the strong maximum principle for
on domains when
is merely a nonnegative Borel function, and then their connection to the existence of a distributional Green's function.
