Suppose that f = (u, v) is a homeomorphism in the plane of the Sobolev class W-loc(1,1) such that its inverse is of the same Sobolev class. We prove that u and v have the same set of critical points. As an application we show that u and v are distributional solutions to the same non-trivial degenerate elliptic equation in divergence form. We study similar properties also in higher dimensions. (c) 2009 Elsevier Inc. All rights reserved.
Bi-sobolev mappings and elliptic equations in the plane
SBORDONE, CARLO
2009-01-01
Abstract
Suppose that f = (u, v) is a homeomorphism in the plane of the Sobolev class W-loc(1,1) such that its inverse is of the same Sobolev class. We prove that u and v have the same set of critical points. As an application we show that u and v are distributional solutions to the same non-trivial degenerate elliptic equation in divergence form. We study similar properties also in higher dimensions. (c) 2009 Elsevier Inc. All rights reserved.File in questo prodotto:
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