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Degenerate Sobolev spaces and regularity of subelliptic equations
Author(s):
Eric
T.
Sawyer;
Richard
L.
Wheeden
Journal:
Trans. Amer. Math. Soc.
MSC (2000):
Primary 35B65, 35D10, 35H20, 46E35
Posted:
October 30, 2009
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Abstract:
We develop a notion of degenerate Sobolev spaces naturally associated with nonnegative quadratic forms that arise from a large class of linear subelliptic equations with rough coefficients. These Sobolev spaces allow us to make the widest possible definition of a weak solution that leads to local Hölder continuity of solutions, extending our results in an earlier work, where we studied regularity of classical weak solutions. In cases when the quadratic forms arise from collections of rough vector fields, we study containment relations between the degenerate Sobolev spaces and the corresponding spaces defined in terms of weak derivatives relative to the vector fields.
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Additional Information:
Eric
T.
Sawyer
Affiliation:
Department of Mathematics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
Richard
L.
Wheeden
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854
DOI:
10.1090/S0002-9947-09-04756-4
PII:
S 0002-9947(09)04756-4
Received by editor(s):
September 6, 2007
Posted:
October 30, 2009
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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