Distance Functions and Almost Global Solutions of Eikonal Equations
نویسندگان
چکیده
منابع مشابه
Distance Functions and Almost Global Solutions of Eikonal Equations
Consider a function u defined on Rn, except, perhaps, on a closed set of potential singularities S. Suppose that u solves the eikonal equation ‖Du‖ = 1 in the pointwise sense on Rn \S, where Du denotes the gradient of u and ‖ · ‖ is a norm on Rn with the dual norm ‖ · ‖∗. For a class of norms which includes the standard p-norms on Rn, 1 < p < ∞, we show that if S has Hausdorff 1-measure zero an...
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ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2010
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605300903253927