Parabolic Capacity and Sobolev Spaces.
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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In recent years, parabolic variational inequalities V.I. have been intensively developed in a functional analytic setting involving many function spaces. As in the case of elliptic V.I., the tools of potential theory have also proven to be most useful for solving and interpreting parabolic V.I. Several facts exhibit a close relationship between the functional analytic and potential theoretic approaches. Among them is the result provided in this paper. Let us describe its content. Just as for the Laplacian operator, a capacity had been associated with the heat operator in order to solve various problems in potential theory. On the other hand, functional spaces - mainly Sobolev spaces, had been introduced to solve variational inequalities involving the heat operator. We prove here that this capacity can be defined in terms of the topology naturally induced by these functional spaces. This leads to interesting new results for parabolic variational inequalities. Author
- Theoretical Mathematics