Smoothness of certain degenerate elliptic equations
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- by John L. Lewis PDF
- Proc. Amer. Math. Soc. 80 (1980), 259-265 Request permission
Abstract:
Given $p > 1,p \ne 2$, let u be a solution to ${\text {div}}(|{\text {grad}}\;u{|^{P - 2}}{\text {grad}}\;u) = 0$ 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.References
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- John L. Lewis, Capacitary functions in convex rings, Arch. Rational Mech. Anal. 66 (1977), no. 3, 201–224. MR 477094, DOI 10.1007/BF00250671
- K. Uhlenbeck, Regularity for a class of non-linear elliptic systems, Acta Math. 138 (1977), no. 3-4, 219–240. MR 474389, DOI 10.1007/BF02392316
- N. N. Ural′ceva, Degenerate quasilinear elliptic systems, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 7 (1968), 184–222 (Russian). MR 0244628
Additional Information
- © Copyright 1980 American Mathematical Society
- 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