Maximal Sobolev regularity for solutions of elliptic equations in infinite dimensional Banach spaces endowed with a weighted Gaussian measure

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• 作者：G. Cappa ^{gianluca.cappa@nemo.unipr.it" class="auth_mail" title="E-mail the corresponding author} ; S. Ferrari ; ^{simone.ferrari1@unipr.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：28C20 ; 35D30 ; 35D35 ; 35J15 ; 46G12
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 December 2016
• 年：2016
• 卷：261
• 期：12
• 页码：7099-7131
• 全文大小：447 K

文摘

Let X be a separable Banach space endowed with a non-degenerate centered Gaussian measure μ. The associated Cameron–Martin space is denoted by H  . Let ν=e^−Uμ$\nu =e^{-U}\mu$, where U:X→R$U:X\to \mathbb{R}$ is a sufficiently regular convex and continuous function. In this paper we are interested in the W^2,2$W^{2,2}$ regularity of the weak solutions of elliptic equations of the type where λ>0$\lambda >0$, f∈L²(X,ν)$f\in {\mathrm{L}}^2(X,\nu )$ and L_ν$L_{\nu }$ is the self-adjoint operator associated with the quadratic form