A $C^1$ regularity result for the inhomogeneous normalized infinity Laplacian
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- by Graziano Crasta and Ilaria Fragalà
- Proc. Amer. Math. Soc. 144 (2016), 2547-2558
- DOI: https://doi.org/10.1090/proc/12916
- Published electronically: October 22, 2015
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Abstract:
We prove that the unique solution to the Dirichlet problem with constant source term for the inhomogeneous normalized infinity Laplacian on a convex domain of $\mathbb {R}^N$ is of class $C^1$. The result is obtained by showing as an intermediate step the power-concavity (of exponent $1/2$) of the solution.References
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Bibliographic Information
- Graziano Crasta
- Affiliation: Dipartimento di Matematica “G. Castelnuovo”, Univ. di Roma I, P.le A. Moro 2 – 00185 Roma, Italy
- MR Author ID: 355300
- ORCID: 0000-0003-3673-6549
- Email: crasta@mat.uniroma1.it
- Ilaria Fragalà
- Affiliation: Dipartimento di Matematica, Politecnico, Piazza Leonardo da Vinci, 32 –20133 Milano, Italy
- MR Author ID: 629098
- Email: ilaria.fragala@polimi.it
- Received by editor(s): July 9, 2015
- Received by editor(s) in revised form: July 17, 2015
- Published electronically: October 22, 2015
- Communicated by: Joachim Krieger
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2547-2558
- MSC (2010): Primary 49K20; Secondary 35J57, 35J70, 49N60
- DOI: https://doi.org/10.1090/proc/12916
- MathSciNet review: 3477071