In:
Communications on Pure and Applied Mathematics, Wiley, Vol. 56, No. 7 ( 2003-07), p. 926-955
Abstract:
We study Plateau's problem for two‐dimensional parametric integrals the Lagrangian F ( x, z ) of which is positive definite and at least semi‐elliptic. It turns out that there always exists a conformally para‐me‐trized minimizer. Any such minimizer X is seen to be Hölder‐continuous in the parameter domain B and continuous up to its boundary. If F possesses a perfect dominance function G of class C 2 , we can establish higher regularity of X in the interior. In fact, we prove X ⊆ H loc 2,2 ( B , ℝ n ) ∩ C 1,σ ( B , ℝ n ) for some σ 〉 0. Finally, we discuss the existence of perfect dominance functions.
Type of Medium:
Online Resource
ISSN:
0010-3640
,
1097-0312
Language:
English
Publisher:
Wiley
Publication Date:
2003
detail.hit.zdb_id:
1468142-0
detail.hit.zdb_id:
1568-4
detail.hit.zdb_id:
220318-2
SSG:
17,1
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