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A theorem of real analysis and its application to free boundary problems
Author(s) -
Athanasopoulos Ioannis,
Caffarelli Luis A.
Publication year - 1985
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160380503
Subject(s) - mathematics , monotone polygon , a priori and a posteriori , boundary (topology) , simple (philosophy) , mathematical analysis , pure mathematics , geometry , philosophy , epistemology
In this note we show how comparison theorems for solutions to equations with non‐smooth coefficients yield in a very simple fashion some free boundary regularity theorems in cases where there is a priori geometrical information, for instance, when one knows that the solution, u , is monotone in some given direction.
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