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arXiv · 1012.1239

Smooth Contractive Embeddings and Application to Feynman Formula for Parabolic Equations on Smooth Bounded Domains

Benedict Baur·Florian Conrad·Martin Grothaus
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Abstract

We prove two assumptions made in an article by Ya.A. Butko, M. Grothaus, O.G. Smolyanov concerning the existence of a strongly continuous operator semigroup solving a Cauchy-Dirichlet problem for an elliptic differential operator in a bounded domain and the existence of a smooth contractive embedding of a core of the generator of the semigroup into the space $C_c^{2,α}(\R^n)$. Based on these assumptions a Feynman formula for the solution of the Cauchy-Dirichlet problem is constructed in the article mentioned above. In this article we show that the assumptions are fulfilled for domains with $C^{4,α}$-smooth boundary and coefficients in $C^{2,α}$.

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BibTeXRIS

Benedict Baur, Florian Conrad, Martin Grothaus. 2010-12-06. Smooth Contractive Embeddings and Application to Feynman Formula for Parabolic Equations on Smooth Bounded Domains. https://doi.org/10.1080/03610926.2011.581170

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