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A note on entire solutions of the eiconal equation
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In this paper, the product 2uu is the derivative of u2; integrating by parts changes (5) into 1 v A1 < 21 (1-u2sin2s)ds, clearly < Fr/2.Abstract:
A1< 2| [u2(sin2s-COS2S)2uusinscoss-u2sin2s+1]ds. (S) The product 2uu is the derivative of u2; integrating by parts changes (5) into 1 v A1< 21 (1-u2sin2s)ds, clearly < Fr/2. Equality holds only if u O, which makes y(s) constant sin s. Since equality in (3) holds only if y = x = 21 _ y2, y(5) _ sin s, x(s) + cos s + constant. This is a semicircle. Q.e.d. Courant Institute of Mathematical Sciences New York Uniuersity 251 Mercer Street New York, NY 10012read more
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Entire and meromorphic solutions of fermat type partial differential equations
Journal ArticleDOI
Distance Functions and Almost Global Solutions of Eikonal Equations
TL;DR: For a class of norms which includes the standard p-norms on n, the authors showed that if u has Hausdorff 1-measure zero and n ≥ 2, then u is either affine or a cone function.
Journal ArticleDOI
On meromorphic solutions of f2 + g2 = 1
TL;DR: In this article, it was shown that the meromorphic solutions f, g of f2 + g2 = 1 in C2 must be constant, if fz2 and gz1 have the same zeros (counting multiplicities).
Journal ArticleDOI
Entire solutions of certain partial differential equations and factorization of partial derivatives
TL;DR: In this paper, it was shown that the problem of characterizing entire solutions of certain partial differential equations and common right factors of partial derivatives of meromorphic functions in C 2 are closely related, and characterizations will be given using their relations.
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Solutions of Complex Fermat-Type Partial Difference and Differential-Difference Equations
Ling Xu,Ting-Bin Cao +1 more
TL;DR: In this paper, the authors investigated the entire and meromorphic solutions of the Fermat-type functional equations such as partial differential-difference equation and partial difference equation by making use of Nevanlinna theory for meromorphic functions in several complex variables.
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