-
Previous Article
Bang-bang property of time optimal controls of semilinear parabolic equation
- DCDS Home
- This Issue
-
Next Article
Holonomies and cohomology for cocycles over partially hyperbolic diffeomorphisms
Lipschitz continuity of free boundary in the continuous casting problem with divergence form elliptic equation
1. | School of Mathematics, University of Edinburgh, King's Buildings, Mayfield Road, EH9 3JZ, Edinburgh, Scotland, United Kingdom |
References:
[1] |
J. Bear, Dynamics of fluids in porous media, Courier Dover Publications, 1988. |
[2] |
L. Caffarelli and S. Salsa, A Geometric Approach to Free Boundary Problems, Graduate Studies in Mathematics, vol. 68 AMS, 2005.
doi: 10.1090/gsm/068. |
[3] |
X. Chen and F. Yi, Regularity of the free boundary of a continuous casting problem, Nonlinear Anal., 21 (1993), 425-438.
doi: 10.1016/0362-546X(93)90126-D. |
[4] |
E. DiBenedetto and M. O'Leary, Three-dimensional conduction-convection problems with change of phase, Arch. Rational Mech. Anal., 123 (1993), 99-116.
doi: 10.1007/BF00695273. |
[5] |
A. Friedman, Variational Principles and Free Boundary Problems, John Wiley & Sons, 1982. |
[6] |
J. Frehse, Capacity methods in the theory of partial differential equations, Jahresbericht der Deutschen Math.-Ver., 84 (1982), 1-44. |
[7] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Reprint of the 1998 edition. Classics in Mathematics. Springer-Verlag, Berlin, 2001. |
[8] |
A. Karakhanyan, On the Lipschitz regularity of solutions of a minimum problem with free boundary, Interfaces Free Bound, 10 (2008), 79-86.
doi: 10.4171/IFB/180. |
[9] |
A. Karakhanyan, Optimal regularity for phase transition problems with convection, Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, in press, 2014.
doi: 10.1016/j.anihpc.2014.03.003. |
[10] |
A. Karakhanyan and J.-F. Rodrigues, The Stefan problem with constant convection, preprint, available online at http://www.maths.ed.ac.uk/~aram/p13.pdf. |
[11] |
J.-F. Rodrigues, Variational methods in the Stefan problem, in Phase transitions and hysteresis (Montecatini Terme, 1993), Lecture Notes in Math., Springer, Berlin, 1584 (1994), 147-212,
doi: 10.1007/BFb0073397. |
[12] |
J.-F. Rodrigues, Obstacle Problems in Mathematical Physics, North-Holland Mathematics Studies, 134. Notas de Matemática, 114. North-Holland Publishing Co., Amsterdam, 1987. |
show all references
References:
[1] |
J. Bear, Dynamics of fluids in porous media, Courier Dover Publications, 1988. |
[2] |
L. Caffarelli and S. Salsa, A Geometric Approach to Free Boundary Problems, Graduate Studies in Mathematics, vol. 68 AMS, 2005.
doi: 10.1090/gsm/068. |
[3] |
X. Chen and F. Yi, Regularity of the free boundary of a continuous casting problem, Nonlinear Anal., 21 (1993), 425-438.
doi: 10.1016/0362-546X(93)90126-D. |
[4] |
E. DiBenedetto and M. O'Leary, Three-dimensional conduction-convection problems with change of phase, Arch. Rational Mech. Anal., 123 (1993), 99-116.
doi: 10.1007/BF00695273. |
[5] |
A. Friedman, Variational Principles and Free Boundary Problems, John Wiley & Sons, 1982. |
[6] |
J. Frehse, Capacity methods in the theory of partial differential equations, Jahresbericht der Deutschen Math.-Ver., 84 (1982), 1-44. |
[7] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Reprint of the 1998 edition. Classics in Mathematics. Springer-Verlag, Berlin, 2001. |
[8] |
A. Karakhanyan, On the Lipschitz regularity of solutions of a minimum problem with free boundary, Interfaces Free Bound, 10 (2008), 79-86.
doi: 10.4171/IFB/180. |
[9] |
A. Karakhanyan, Optimal regularity for phase transition problems with convection, Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, in press, 2014.
doi: 10.1016/j.anihpc.2014.03.003. |
[10] |
A. Karakhanyan and J.-F. Rodrigues, The Stefan problem with constant convection, preprint, available online at http://www.maths.ed.ac.uk/~aram/p13.pdf. |
[11] |
J.-F. Rodrigues, Variational methods in the Stefan problem, in Phase transitions and hysteresis (Montecatini Terme, 1993), Lecture Notes in Math., Springer, Berlin, 1584 (1994), 147-212,
doi: 10.1007/BFb0073397. |
[12] |
J.-F. Rodrigues, Obstacle Problems in Mathematical Physics, North-Holland Mathematics Studies, 134. Notas de Matemática, 114. North-Holland Publishing Co., Amsterdam, 1987. |
[1] |
Donatella Danielli, Marianne Korten. On the pointwise jump condition at the free boundary in the 1-phase Stefan problem. Communications on Pure and Applied Analysis, 2005, 4 (2) : 357-366. doi: 10.3934/cpaa.2005.4.357 |
[2] |
Toyohiko Aiki. A free boundary problem for an elastic material. Conference Publications, 2007, 2007 (Special) : 10-17. doi: 10.3934/proc.2007.2007.10 |
[3] |
Yang Zhang. A free boundary problem of the cancer invasion. Discrete and Continuous Dynamical Systems - B, 2022, 27 (3) : 1323-1343. doi: 10.3934/dcdsb.2021092 |
[4] |
Hayk Mikayelyan, Henrik Shahgholian. Convexity of the free boundary for an exterior free boundary problem involving the perimeter. Communications on Pure and Applied Analysis, 2013, 12 (3) : 1431-1443. doi: 10.3934/cpaa.2013.12.1431 |
[5] |
Michael L. Frankel, Victor Roytburd. Fractal dimension of attractors for a Stefan problem. Conference Publications, 2003, 2003 (Special) : 281-287. doi: 10.3934/proc.2003.2003.281 |
[6] |
Lincoln Chayes, Inwon C. Kim. The supercooled Stefan problem in one dimension. Communications on Pure and Applied Analysis, 2012, 11 (2) : 845-859. doi: 10.3934/cpaa.2012.11.845 |
[7] |
Piotr B. Mucha. Limit of kinetic term for a Stefan problem. Conference Publications, 2007, 2007 (Special) : 741-750. doi: 10.3934/proc.2007.2007.741 |
[8] |
Xiaoshan Chen, Fahuai Yi. Free boundary problem of Barenblatt equation in stochastic control. Discrete and Continuous Dynamical Systems - B, 2016, 21 (5) : 1421-1434. doi: 10.3934/dcdsb.2016003 |
[9] |
Naoki Sato, Toyohiko Aiki, Yusuke Murase, Ken Shirakawa. A one dimensional free boundary problem for adsorption phenomena. Networks and Heterogeneous Media, 2014, 9 (4) : 655-668. doi: 10.3934/nhm.2014.9.655 |
[10] |
Yongzhi Xu. A free boundary problem model of ductal carcinoma in situ. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 337-348. doi: 10.3934/dcdsb.2004.4.337 |
[11] |
Anna Lisa Amadori. Contour enhancement via a singular free boundary problem. Conference Publications, 2007, 2007 (Special) : 44-53. doi: 10.3934/proc.2007.2007.44 |
[12] |
Shihe Xu. Analysis of a delayed free boundary problem for tumor growth. Discrete and Continuous Dynamical Systems - B, 2011, 15 (1) : 293-308. doi: 10.3934/dcdsb.2011.15.293 |
[13] |
Chonghu Guan, Xun Li, Rui Zhou, Wenxin Zhou. Free boundary problem for an optimal investment problem with a borrowing constraint. Journal of Industrial and Management Optimization, 2022, 18 (3) : 1915-1934. doi: 10.3934/jimo.2021049 |
[14] |
Hiroshi Matsuzawa. A free boundary problem for the Fisher-KPP equation with a given moving boundary. Communications on Pure and Applied Analysis, 2018, 17 (5) : 1821-1852. doi: 10.3934/cpaa.2018087 |
[15] |
Micah Webster, Patrick Guidotti. Boundary dynamics of a two-dimensional diffusive free boundary problem. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 713-736. doi: 10.3934/dcds.2010.26.713 |
[16] |
Jan Prüss, Jürgen Saal, Gieri Simonett. Singular limits for the two-phase Stefan problem. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5379-5405. doi: 10.3934/dcds.2013.33.5379 |
[17] |
Marianne Korten, Charles N. Moore. Regularity for solutions of the two-phase Stefan problem. Communications on Pure and Applied Analysis, 2008, 7 (3) : 591-600. doi: 10.3934/cpaa.2008.7.591 |
[18] |
Karl P. Hadeler. Stefan problem, traveling fronts, and epidemic spread. Discrete and Continuous Dynamical Systems - B, 2016, 21 (2) : 417-436. doi: 10.3934/dcdsb.2016.21.417 |
[19] |
Junde Wu. Bifurcation for a free boundary problem modeling the growth of necrotic multilayered tumors. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3399-3411. doi: 10.3934/dcds.2019140 |
[20] |
Maho Endo, Yuki Kaneko, Yoshio Yamada. Free boundary problem for a reaction-diffusion equation with positive bistable nonlinearity. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3375-3394. doi: 10.3934/dcds.2020033 |
2021 Impact Factor: 1.588
Tools
Metrics
Other articles
by authors
[Back to Top]