Strong Comparison Principle for the Fractional p-Laplacian and Applications to Starshaped Rings

被引:29
|
作者
Jarohs, Sven [1 ]
机构
[1] Goethe Univ, Frankfurt, Germany
关键词
Fractional p-Laplacian; Strong Comparison Principle; Starshaped Superlevel Sets;
D O I
10.1515/ans-2017-6039
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In the following, we show the strong comparison principle for the fractional p-Laplacian, i.e. we analyze {(-Delta)(p)(s)v + q(x)vertical bar v vertical bar(p-2) v >= 0 in D, (-Delta(s)(p)w + q(x)vertical bar w vertical bar(p-2) w <= 0 in D, v >= w in R-N, where s is an element of (0, 1), p > 1, D subset of R-N is an open set, and q is an element of L-infinity (R-N) is a nonnegative function. Under suitable conditions on s, p and some regularity assumptions on v, w, we show that either v w in R-N or v > w in D. Moreover, we apply this result to analyze the geometry of nonnegative solutions in starshaped rings and in the half space.
引用
收藏
页码:691 / 704
页数:14
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