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For a $C^2$ function $u$ and an elliptic operator $L$, we prove a quantitative estimate for the derivative $du$ in terms of local bounds on $u$ and $Lu$. An integral… Click to show full abstract
For a $C^2$ function $u$ and an elliptic operator $L$, we prove a quantitative estimate for the derivative $du$ in terms of local bounds on $u$ and $Lu$. An integral version of this estimate is then used to derive a condition for the zero-mean value property of $\Delta u$. An extension to differential forms is also given. Our approach is probabilistic and could easily be adapted to other settings.
Keywords:
bismut formulae;
estimates bismut;
quantitative estimates
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2018
Link to full text (if available)
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!