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NCTS Differential Geometry Seminar
 
16:00 - 17:00, March 8, 2018 (Thursday)
Room 440, 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.


 

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