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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Smoothness of certain degenerate elliptic equations


Author: John L. Lewis
Journal: Proc. Amer. Math. Soc. 80 (1980), 259-265
MSC: Primary 35J70
DOI: https://doi.org/10.1090/S0002-9939-1980-0577755-6
MathSciNet review: 577755
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Abstract: Given $ p > 1,p \ne 2$, let u be a solution to $ {\text{div}}(\vert{\text{grad}}\;u{\vert^{P - 2}}{\text{grad}}\;u) = 0$ on a domain D in Euclidean two space. We prove that if u is nonconstant and real analytic in D, then the gradient of u does not vanish in D. Some examples of Krol' are used to show this result and a related result of Ural'tseva are nearly best possible.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0577755-6
Keywords: Real analyticity, degenerate elliptic equations of divergence type
Article copyright: © Copyright 1980 American Mathematical Society

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