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Global L∞ gradient estimates for solutions to a certain degenerate elliptic equation

Brasco, Lorenzo (2011), Global L∞ gradient estimates for solutions to a certain degenerate elliptic equation, Nonlinear Analysis: Theory, Methods & Applications, 74, 2, p. 511-531. http://dx.doi.org/10.1016/j.na.2010.09.006

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Type
Article accepté pour publication ou publié
Date
2011
Journal name
Nonlinear Analysis: Theory, Methods & Applications
Volume
74
Number
2
Publisher
Elsevier
Pages
511-531
Publication identifier
Metadata
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Author(s)
Brasco, Lorenzo
Abstract (EN)
In view of the applications in the study of regularity properties of minimizers for a continuous model of transportation, which is a kind of divergence-constrained optimization problem, we prove a global L∞ gradient estimate for solutions of an elliptic equation, whose ellipticity constants become degenerate at every point where |∇u|≤δ, with δ>0. The exposition is as self-contained as possible.
Subjects / Keywords
Degenerate elliptic equations; Neumann boundary value problem; Non-convex variational problems; Traffic congestion