A nonlocal p-Laplacian evolution equation with Neumann boundary conditions

Journal des Mathematiques Pures et Appliquees

Volumn 90, Issue 2, 2008, Pages 201-227

  Andreu, F ^a   Mazon J M ^a   Rossi, J D ^b,c   Toledo, J ^a  

^a UNIVERSITY OF VALENCIA   (Spain)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^c UNIVERSIDAD DE BUENOS AIRES   (Argentina)

Author keywords

Neumann boundary conditions; Nonlocal diffusion; p Laplacian; Total variation flow

Indexed keywords

EID: 47349087551     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2008.04.003     Document Type: Article

References (31)

1. Ambrosio L., Fusco N., and Pallara D. Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs (2000), Oxford Univ. Press
2. Andreu F., Ballester C., Caselles V., and Mazon J.M. Minimizing total variation flow. Differential Integral Equations 14 (2001) 321-360
3. Andreu F., Caselles V., and Mazon J.M. Parabolic Quasilinear Equations Minimizing Linear Growth Functionals. Progress in Mathematics vol. 223 (2004), Birkhäuser
4. Andreu F., Igbida N., Mazón J.M., and Toledo J. A degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions. Interfaces and Free Boundaries 8 (2006) 447-479
5. 1 with nonlinear boundary conditions. Adv. Math. Sci. Appl. 7 (1997) 183-213
6. 1-data. Trans. Amer. Math. Soc. 351 1 (1999) 285-306
7. F. Andreu, J.M. Mazón, J.D. Rossi, J. Toledo, The Neumann problem for nonlocal nonlinear diffusion equations, J. Evol. Eqns., in press
8. Bates P., and Chmaj A. An integrodifferential model for phase transitions: Stationary solutions in higher dimensions. J. Statist. Phys. 95 (1999) 1119-1139
9. Bates P., Fife P., Ren X., and Wang X. Travelling waves in a convolution model for phase transitions. Arch. Rat. Mech. Anal. 138 (1997) 105-136
10. Bénilan Ph., and Crandall M.G. Completely accretive operators. Semigroup Theory and Evolution Equations. Delft, 1989. Lecture Notes in Pure and Appl. Math. vol. 135 (1991), Dekker, New York 41-75
11. Ph. Bénilan, M.G. Crandall, A. Pazy, Evolution Equations Governed by Accretive Operators, in press
12. Bourgain J., Brezis H., and Mironescu P. Another look at Sobolev spaces. In: Menaldi J.L., et al. (Ed). Optimal Control and Partial Differential Equations, vol. A (2001), IOS Press 439-455 (in honour of A. Bensoussan's 60th birthday)
13. Brezis H. Équations et inéquations non linéaires dans les espaces vectoriels en dualité. Ann. Inst. Fourier 18 (1968) 115-175
14. Buades A., Coll B., and Morel J.M. Neighborhood filters and PDE's. Numer. Math. 150 (2006) 1-34
15. Carrillo C., and Fife P. Spatial effects in discrete generation population models. J. Math. Biol. 50 2 (2005) 161-188
16. Chasseigne E., Chaves M., and Rossi J.D. Asymptotic behaviour for nonlocal diffusion equations. J. Math. Pures Appl. 86 (2006) 271-291
17. Chen X. Existence, uniqueness and asymptotic stability of travelling waves in nonlocal evolution equations. Adv. Differential Equations 2 (1997) 125-160
18. Cortazar C., Elgueta M., and Rossi J.D. A non-local diffusion equation whose solutions develop a free boundary. Ann. Henri Poincaré 6 2 (2005) 269-281
19. Cortazar C., Elgueta M., Rossi J.D., and Wolanski N. Boundary fluxes for non-local diffusion. J. Differential Equations 234 (2007) 360-390
20. Cortazar C., Elgueta M., Rossi J.D., and Wolanski N. How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems. Arch. Rat. Mech. Anal. 187 (2008) 137-156
21. Crandall M.G. Nonlinear semigroups and evolution governed by accretive operators. In: Browder F. (Ed). Proc. of Sympos. in Pure Mathematics vol. 45 (1986), Amer. Math. Soc., Providence 305-338 (Part I)
22. Fife P. Some nonclassical trends in parabolic and parabolic-like evolutions. Trends in Nonlinear Analysis (2003), Springer, Berlin 153-191
23. Fife P., and Wang X. A convolution model for interfacial motion: The generation and propagation of internal layers in higher space dimensions. Adv. Differential Equations 3 1 (1998) 85-110
24. Kindermann S., Osher S., and Jones P.W. Deblurring and denoising of images by nonlocal functionals. Multiscale Model. Simul. 4 (2005) 1091-1115
25. Rudin L., Osher S., and Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D 60 (1992) 259-268
26. Silvestre L. Hölder estimates for solutions of integrodifferential equations like the fractional Laplace. Indiana Univ. Math. J. 55 3 (2006) 1155-1174
27. C. Tomasi, R. Manduchi, Bilateral filtering for gray and color images, in: Proceedings of the Sixth International Conference on Computer Vision, Bombay, India, 1998, pp. 839-846
28. Wang X. Metastability and stability of patterns in a convolution model for phase transitions. J. Differential Equations 183 (2002) 434-461
29. Yaroslavsky L.P. Digital Picture Processing. An Introduction (1985), Springer, Berlin
30. Yaroslavsky L.P., and Eden M. Fundamentals of Digital Optics (1996), Birkhäuser, Boston
31. Zhang L. Existence, uniqueness and exponential stability of traveling wave solutions of some integral differential equations arising from neuronal networks. J. Differential Equations 197 1 (2004) 162-196