Stability for parabolic quasi minimizers in metric measure spaces
Yohei Fujishima
Shizuoka University, Hamamatsu, JapanJens Habermann
Universität Erlangen-Nürnberg, Germany
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Abstract
We are concerned with the stability property for parabolic quasi minimizers in metric measure spaces. More precisely we consider a doubling metric measure space which supports a weak Poincaré inequality and a parabolic domain on the product space , where is a domain whose boundary is regular in the sense that its complement satisfies a uniform capacity density condition. We then show that a parabolic quasi minimizer of the energy, , with fixed initial boundary data on the parabolic boundary of is stable with respect to the variation of and . The manuscript at hand is an extension of the result [7] to the setting of metric measure spaces.
Cite this article
Yohei Fujishima, Jens Habermann, Stability for parabolic quasi minimizers in metric measure spaces. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), no. 2, pp. 343–376
DOI 10.4171/RLM/810