Open Access
Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 46 | |
Number of page(s) | 29 | |
DOI | https://doi.org/10.1051/cocv/2024034 | |
Published online | 04 June 2024 |
- W. Fulks, An approximate Gauss mean value theorem. Pac. J. Math. 14 (1964) 513–516. [CrossRef] [Google Scholar]
- N. Kuznetsov, Mean value properties of harmonic functions and related topics (a survey). J. Math. Sci. 242 (2019) 177–199. [CrossRef] [MathSciNet] [Google Scholar]
- I. Netuka and J. Veselý, Mean value property and harmonic functions, Classical and modern potential theory and applications (Chateau de Bonas, 1993). NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 430, Kluwer Acad. Publ., Dordrecht (1994) 359–398. [Google Scholar]
- E. Le Gruyer, On absolutely minimizing Lipschitz extensions and PDE ∆∞(u) = 0. Nonlinear Differ. Equ. Appl. 14 (2007) 29–55. [CrossRef] [Google Scholar]
- H. Luiro, M. Parviainen and E. Saksman, On the existence and uniqueness of p-harmonious functions. Differ. Integral Equ. 27 (2014) 201–216. [Google Scholar]
- J.J. Manfredi, M. Parviainen and J.D. Rossi, An asymptotic mean value characterization for p-harmonic functions. Proc. Amer. Math. Soc. 138 (2010) 881–889. [Google Scholar]
- J.J. Manfredi, M. Parviainen and J.D. Rossi, An asymptotic mean value characterization for a class of nonlinear parabolic equations related to tug-of-war games. SIAM J. Math. Anal. 42 (2010) 2058–2081. [CrossRef] [MathSciNet] [Google Scholar]
- J.J. Manfredi, M. Parviainen and J.D. Rossi, On the definition and properties of p-harmonious functions. Ann. Sci. Norm. Super. Pisa Cl. Sci. 11 (2012) 215–241. [MathSciNet] [Google Scholar]
- M. Ishiwata, R. Magnanini and H. Wadade, A natural approach to the asymptotic mean value property for the p-Laplacian. Calc. Var. Partial Differ. Equ. 56 (2017) 56–97. [CrossRef] [Google Scholar]
- D. Hartenstine and M. Rudd, Asymptotic statistical characterizations of p-harmonic functions of two variables. Rocky Mountain J. Math. 41 (2011) 493–504. [CrossRef] [MathSciNet] [Google Scholar]
- M. Rudd and H. Van Dyke, Median values, 1-harmonic functions, and functions of least gradient. Commun. Pure Appl. Anal. 12 (2013) 711–719. [Google Scholar]
- S.G. Noah, The median of a continuous function. Real Anal. Exchange 33 (2008) 269–274. [CrossRef] [MathSciNet] [Google Scholar]
- I. Al-Awamleh, Mean value properties for p-harmonic functions for higher dimensions. J. Elliptic Parabolic Equ. 9 (2023) 315–329. [CrossRef] [MathSciNet] [Google Scholar]
- I. Al-Awamleh and R. Smits, Statistical and algebraic properties for the 4-Laplacian via averaging. arXiv:2303.06134 (2023). [Google Scholar]
- A. Arroyo and M. Parviainen, Hölder estimates for a tug-of-war game with 1 < p < 2 from Krylov–Safonov regularity theory Rev. Mat. Iberoam. (2024) online first DOI 10.4171/RMI/1462, preprint arXiv:2212.10807 (2022). [Google Scholar]
- T. Giorgi and R. Smits, Mean value property for p-harmonic functions. Proc. Amer. Math. Soc. 140 (2012) 2453–2463. [Google Scholar]
- F. del Teso and E. Lindgren, A mean value formula for the variational p-Laplacian. Nonlinear Differ. Equ. Appl. 28 (2021) 27. [CrossRef] [Google Scholar]
- C. Bucur and M. Squassina, An asymptotic expansion for the fractional p-Laplacian and for gradient dependent nonlocal operators. Commun. Contemp. Math. 24 (2022) 2150021. [CrossRef] [Google Scholar]
- F. del Teso, M. Medina and P. Ochoa, Higher-order asymptotic expansions and finite difference schemes for the fractional p-Laplacian. Math. Ann. (2023). [Google Scholar]
- F. Ferrari, Mean value properties of fractional second order operators. Commun. Pure Appl. Anal. 14 (2015) 83–106. [Google Scholar]
- C. Fjellström, K. Nyström and Y. Wang, Asymptotic mean value formulas, nonlocal space-time parabolic operators and anomalous tug-of-war games. J. Differ. Equ. 342 (2023) 150–178. [CrossRef] [Google Scholar]
- W. Meng and C. Zhang, Aymptotic mean value properties for the elliptic and parabolic double phase equations. Nonlinear Differ. Equ. Appl. 30 (2023) 77. [CrossRef] [Google Scholar]
- P. Blanc, F. Charro, J.J. Manfredi and J.D. Rossi, Asymptotic mean-value formulas for solutions of general second-order elliptic equations. Adv. Nonlinear Stud. 22 (2022) 118–142. [CrossRef] [MathSciNet] [Google Scholar]
- N. Kuznetsov, Mean value properties of solutions to the Helmholtz and modified Helmholtz equations. J. Math. Sci. 257 (2021) 673–683. [CrossRef] [MathSciNet] [Google Scholar]
- P. Blanc, F. Charro, J.J. Manfredi and J.D. Rossi, A nonlinear mean value property for the Monge–Ampère operator. J. Convex Anal. 28 (2021) 353–386. [MathSciNet] [Google Scholar]
- T. Adamowicz, A. Kijowski and E. Soultanis, Asymptotically mean value harmonic functions in doubling metric measure spaces. Anal. Geom. Metric Spaces 10 (2022) 344–372. [CrossRef] [MathSciNet] [Google Scholar]
- T. Adamowicz, A. Kijowski and E. Soultanis, Asymptotically mean value harmonic functions in sub Riemannian and RCD settings. J. Geom. Anal. 33 (2023) 80. [CrossRef] [Google Scholar]
- A. Minne and D. Tewodrose, Symmetrized and non-symmetrized asymptotic mean value Laplacian in metric measure spaces. arXiv:2202.09295 (2023). [Google Scholar]
- E.W. Chandra, M. Ishiwata, R. Magnanini and H. Wadade, Variational p-harmonious functions: existence and convergence to p-harmonic functions. Nonlinear Differ. Equ. Appl. 28 (2021) 51. [CrossRef] [Google Scholar]
- F. del Teso, J.J. Manfredi and M. Parviainen, Convergence of dynamic programming principles for the p-Laplacian. Adv. Calc. Var. 15 (2022) 191–212. [CrossRef] [MathSciNet] [Google Scholar]
- D. Hartenstine and M. Rudd, Statistical functional equations and p-harmonious functions. Adv. Nonlinear Stud. 13 (2013) 191–207. [CrossRef] [MathSciNet] [Google Scholar]
- D. Hartenstine and M. Rudd, Perron’s method for p-harmonious functions. Electron. J. Differ. Equ. 2016 (2016) 1–12. [CrossRef] [Google Scholar]
- A. Domokos, J.J. Manfredi, D. Ricciotti and B. Stroffolini, Convergence of natural p-means for the p-Laplacian in the Heisenberg group. Nonlinear Anal. 223 (2022) 113058. [CrossRef] [Google Scholar]
- J.J. Manfredi and B. Stroffolini, Convergence of the natural p-means for the p-Laplacian. ESAIM Control Optim. Calc. Var. 27 (2021) Paper No. 33. [CrossRef] [EDP Sciences] [Google Scholar]
- T. Adamowicz, A. Kijowski, A. Pinamonti and B. Warhurst, Variational approach to the asymptotic mean-value property for the p-Laplacian on Carnot groups. Nonlin. Anal. 198 (2020) 111893. [CrossRef] [Google Scholar]
- F. Ferrari and N. Forcillo, Alt-Caffarelli-Friedman monotonicity formula and mean value properties in Carnot groups with applications. Boll. Unione Mat. Ital. (2023). [Google Scholar]
- F. Ferrari and A. Pinamonti, Characterization by asymptotic mean formulas of q-harmonic functions in Carnot groups. Potential Anal. 42 (2015) 203–227. [CrossRef] [MathSciNet] [Google Scholar]
- D. Pallara and S. Polidoro, Mean value formulas for classical solutions to some degenerate elliptic equations in Carnot groups. Discrete Continuous Dyn. Syst. S (2022) https://10.3934/dcdss.2022144. [Google Scholar]
- Y. Bai and L. Wu, New properties of complex functions with mean value conditions. Abstr. Appl. Anal. 11 (2011) 167160. [CrossRef] [Google Scholar]
- N. Katzourakis, On a vector-valued generalisation of viscosity solutions for general PDE systems. Z. Anal. Anwend. 41 (2022) 93–132. [CrossRef] [MathSciNet] [Google Scholar]
- H. Luiro and M. Parviainen, Regularity for nonlinear stochastic games. Ann. Inst. H. Poincaré C Anal. Non Linéaire 35 (2018) 1435–1456. [CrossRef] [MathSciNet] [Google Scholar]
- T. Iwaniec and J.J. Manfredi, Regularity of p-harmonic functions on the plane. Rev. Mat. Iberoamericana 5 (1989) 1–19. [CrossRef] [MathSciNet] [Google Scholar]
- G. Alessandrini, D. Lupo and E. Rosset, Local behavior and geometric properties of solutions to degenerate quasilinear elliptic equation in the plane. Appl. Anal. 50 (1993) 191–215. [CrossRef] [MathSciNet] [Google Scholar]
- B. Bojarski and T. Iwaniec, p-harmonic equation and quasiregular mappings. Banach Center Publ. 19 (1987) 25–38. [CrossRef] [Google Scholar]
- G. Aronsson and P. Lindqvist, On p-harmonic functions in the plane and their stream functions. J. Differ. Equ. 74 (1988) 157–178. [CrossRef] [Google Scholar]
- G. Aronsson, Representation of p-harmonic function near critical point in the plane. Manuscripta Math. 66 (1989) 73–95. [Google Scholar]
- J.J. Manfredi, p-harmonic functions in the plane. Proc. Amer. Math. Soc. 103 (1988) 473–479. [MathSciNet] [Google Scholar]
- P. Lindqvist and J.J. Manfredi, On the mean value property for the p-Laplace equation in the plane. Proc. Amer. Math. Soc. 144 (2016) 143–149. [Google Scholar]
- A. Arroyo and J.G. Llorente, On the asymptotic mean value property for planar p-harmonic functions. Proc. Amer. Math. Soc. 144 (2016) 3859–3868. [CrossRef] [MathSciNet] [Google Scholar]
- P. Juutinen, P. Lindqvist and J.J. Manfredi, On the equivalence of viscosity solutions and weak solutions for a quasi-linear elliptic equation. SIAM J. Math. Anal. 33 (2001) 699–717. [CrossRef] [MathSciNet] [Google Scholar]
- R. Magnanini and M. Marini, Characterization of ellipses as uniformly dense sets with respect to a family of convex bodies. Ann. Mat. Pura Appl. 193 (2014) 1383–1395. [CrossRef] [MathSciNet] [Google Scholar]
- A.I. Markushevich, Theory of Functions of a Complex Variable. 2nd English edn., Vols. I, II, III. Translated and edited by R.A. Silverman. Chelsea Publishing Co., New York (1977). [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.