We prove Rellich–Kondrachov-type theorems and weighted Poincaré inequalities on the half-space R+N+1={z=(x,y):x∈RN,y>0} endowed with the weighted Gaussian measure μ:=yce-a|z|2dz where c+1>0 and a>0. We prove that for some positive constant C>0, one has (Formula presented.) where u¯=1μ(R+N+1)∫R+N+1udμ(z). Besides this, we also consider the local case of bounded domains of R+N+1 where the measure μ is ycdz.
Gaussian Poincare Inequalities on the Half-Space with Singular Weights
Negro L.
;Spina C.
2025-01-01
Abstract
We prove Rellich–Kondrachov-type theorems and weighted Poincaré inequalities on the half-space R+N+1={z=(x,y):x∈RN,y>0} endowed with the weighted Gaussian measure μ:=yce-a|z|2dz where c+1>0 and a>0. We prove that for some positive constant C>0, one has (Formula presented.) where u¯=1μ(R+N+1)∫R+N+1udμ(z). Besides this, we also consider the local case of bounded domains of R+N+1 where the measure μ is ycdz.File in questo prodotto:
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