Energy Concentration and Sommerfeld Condition for Helmholtz Equation with Variable Index at Infinity
نویسندگان
چکیده
منابع مشابه
Energy concentration and Sommerfeld condition for Helmholtz equation with variable index at infinity
We consider the Helmholtz equation with a variable index of refraction n(x), which is not necessarily constant at infinity but can have an angular dependency like n(x) → n ∞ (x/|x|) as |x| → ∞. Under some appropriate assumptions on this convergence and on n ∞ we prove that the Sommerfeld condition at infinity still holds true under the explicit form R d ∇u − in 1/2 ∞ u x |x| 2 dx |x| < +∞. It i...
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2007
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-007-0635-6