Validity and failure of the integral representation of Γ-limits of convex non-local functionals

被引：0
|
作者：
Braides, Andrea [1 ]
Dal Maso, Gianni [1 ]
机构：
[1] SISSA, Via Bonomea 265, Trieste, Italy
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2024年 / 286卷 / 06期
关键词：
Gamma-convergence; Dirichlet forms; Non-local functionals; Integral representation;
D O I：
10.1016/j.jfa.2024.110317
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove an integral-representation result for limits of non-local quadratic forms on H-0(1)(Omega), with Omega a bounded open subset of R-d, extending the representation on C-c(infinity)(Omega) given by the Beurling Deny formula in the theory of Dirichletforms. We give a counter example showing that a corresponding representation may not hold if we consider analogous functionals in W-0(1,p)(Omega), with p not equal 2and 1 < p <= d
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页数：26
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