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Classifications of Solutions to Some Nonlocal Operators

By Mouhammed Moustapha Fall, African Institute for Mathematical Sciences (AIMS) in Senegal

In the first part of the talk, we will discuss classifications of distributional solutions to general elliptic equations driven by nonlocal operators generated by a stable Lévy process (not necessarily symmetric). In the second part of the talk, we will show how to transform a nonlocal equation to a local one and thus. The argument is based on a kind of 'factorization' property of local operators by many nonlocal operators. This allow us to obtain further classifications of some distributional solutions with possibly variable coefficients. We will present several applications. Joint work with Tobias Weth.