Nonexistence of an a priori bound at the center in terms of an L 1 bound on the boundary for solutions of uniformly elliptic equations on a sphere

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ID: 261719
1970
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Abstract
Positive solutions on the unit sphere of second order uniformly elliptic nonvariational equations are found which exhibit behavior sharply differing from that of positive harmonic functions, despite the fact that the coefficients may be uniformly arbitrarily close (at least for n=2) to those of the Laplacian. A solution is found whose boundary integral on expanding concentric subspheres tends to zero and another is found for which this boundary iutegral tends to infinity.
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miller1970annalinonexistence Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Keith Miller;Keith Miller;
Journal annali di matematica pura ed applicata
Year 1970
DOI
doi:10.1007/BF02415078
URL
https://link.springer.com/article/10.1007/BF02415078
Keywords
mathematics general

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