Schauder theorems for linear elliptic and parabolic problems with unbounded coefficients in
Studia Mathematica (1998)
- Volume: 128, Issue: 2, page 171-198
- ISSN: 0039-3223
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topLunardi, Alessandra. "Schauder theorems for linear elliptic and parabolic problems with unbounded coefficients in $ℝ^{n}$." Studia Mathematica 128.2 (1998): 171-198. <http://eudml.org/doc/216482>.
@article{Lunardi1998,
abstract = {We study existence, uniqueness, and smoothing properties of the solutions to a class of linear second order elliptic and parabolic differential equations with unbounded coefficients in $ℝ^n$. The main results are global Schauder estimates, which hold in spite of the unboundedness of the coefficients.},
author = {Lunardi, Alessandra},
journal = {Studia Mathematica},
keywords = {Schauder estimates},
language = {eng},
number = {2},
pages = {171-198},
title = {Schauder theorems for linear elliptic and parabolic problems with unbounded coefficients in $ℝ^\{n\}$},
url = {http://eudml.org/doc/216482},
volume = {128},
year = {1998},
}
TY - JOUR
AU - Lunardi, Alessandra
TI - Schauder theorems for linear elliptic and parabolic problems with unbounded coefficients in $ℝ^{n}$
JO - Studia Mathematica
PY - 1998
VL - 128
IS - 2
SP - 171
EP - 198
AB - We study existence, uniqueness, and smoothing properties of the solutions to a class of linear second order elliptic and parabolic differential equations with unbounded coefficients in $ℝ^n$. The main results are global Schauder estimates, which hold in spite of the unboundedness of the coefficients.
LA - eng
KW - Schauder estimates
UR - http://eudml.org/doc/216482
ER -
References
top- [1] D. G. Aronson and P. Besala, Parabolic equations with unbounded coefficients, J. Differential Equations 3 (1967), 1-14. Zbl0149.06804
- [2] J. S. Baras, G. O. Blankenship and W. E. Hopkins, Existence, uniqueness and asymptotic behavior of solutions to a class of Zakai equations with unbounded coefficients, IEEE Trans. Automat. Control 28 (1983), 203-214. Zbl0535.93063
- [3] A. Bensoussan and J.-L. Lions, Applications of Variational Inequalities in Stochastic Control, North-Holland, Amsterdam, 1982.
- [4] P. Besala, On the existence of a fundamental solution for a parabolic differential equation with unbounded coefficients, Ann. Polon. Math. 29 (1975), 403-409. Zbl0305.35047
- [5] W. Bodanko, Sur le problème de Cauchy et les problèmes de Fourier pour les équations paraboliques dans un domaine non borné, ibid. 28 (1966), 79-94. Zbl0139.05504
- [6] P. Cannarsa and V. Vespri, Generation of analytic semigroups by elliptic operators with unbounded coefficients, SIAM J. Math. Anal. 18 (1987), 857-872. Zbl0623.47039
- [7] S. Cerrai, Elliptic and parabolic equations in with coefficients having polynomial growth, Comm. Partial Differential Equations 21 (1996), 281-317. Zbl0851.35049
- [8] S. Cerrai, Some results for second order elliptic operators having unbounded coefficients, preprint, Scuola Norm. Sup. Pisa, 1996.
- [9] E. B. Davies, Heat Kernels and Spectral Theory, Cambridge Univ. Press, 1990. Zbl0699.35006
- [10] M. H. Davis and S. I. Markus, An Introduction to Nonlinear Filtering, NATO Adv. Study Inst. Ser., Reidel, Dordrecht, 1980.
- [11] G. Da Prato and A. Lunardi, On the Ornstein-Uhlenbeck operator in spaces of continuous functions, J. Funct. Anal. 131 (1995), 94-114. Zbl0846.47004
- [12] W. H. Fleming and S. K. Mitter, Optimal control and nonlinear filtering for nondegenerate diffusion processes, Stochastics 8 (1982), 63-77. Zbl0493.93047
- [13] S. Ito, Fundamental solutions of parabolic differential equations and boundary value problems, Japan. J. Math. 27 (1957), 5-102.
- [14] A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel, 1995. Zbl0816.35001
- [15] A. Lunardi, An interpolation method to characterize domains of generators of semigroups, Semigroup Forum 53 (1996), 321-329. Zbl0859.47030
- [16] A. Lunardi, On the Ornstein-Uhlenbeck operator in spaces with respect to invariant measures, Trans. Amer. Math. Soc. 349 (1997), 155-169. Zbl0890.35030
- [17] A. Lunardi and V. Vespri, Optimal and Schauder estimates for elliptic and parabolic operators with unbounded coefficients, in: Reaction-Diffusion Systems, Proc., G. Caristi and E. Mitidieri (eds.), Lecture Notes in Pure and Appl. Math. 194, M. Dekker, 1997, 217-239. Zbl0887.47034
- [18] A. Lunardi and V. Vespri, Generation of strongly continuous semigroups by elliptic operators with unbounded coefficients in , Rend. Mat., volume in honour of P. Grisvard, to appear. Zbl0899.35027
- [19] S. J. Sheu, Solution of certain parabolic equations with unbounded coefficients and its application to nonlinear filtering, Stochastics 10 (1983), 31-46. Zbl0533.60068
- [20] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
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