CONTINUOUS FLOW TRANSFER HYDROGENATION OF BIOMASS DERIVED METHYL LEVULINATE OVER ZR CONTAINING ZEOLITES: INSIGHTS INTO THE ROLE OF THE CATALYST ACIDITY
Molecular Catalysis. Elsevier B.V.. Том 477. 2019.
We consider Sobolev problems (problems for an elliptic operator on a closed manifold with conditions on a closed submanifold) for the case in which these conditions are of nonlocal nature and include weighted spherical means of the unknown function over spheres of a given radius. For such problems, we establish a criterion for the Fredholm property and, in some special cases, obtain index formulas. © 2019, Pleiades Publishing, Ltd.