Schauder theorems for linear elliptic and parabolic problems with unbounded coefficients in n

Alessandra Lunardi

Studia Mathematica (1998)

  • Volume: 128, Issue: 2, page 171-198
  • ISSN: 0039-3223

Abstract

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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 n . The main results are global Schauder estimates, which hold in spite of the unboundedness of the coefficients.

How to cite

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Lunardi, 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

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  3. [3] A. Bensoussan and J.-L. Lions, Applications of Variational Inequalities in Stochastic Control, North-Holland, Amsterdam, 1982. 
  4. [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
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  15. [15] A. Lunardi, An interpolation method to characterize domains of generators of semigroups, Semigroup Forum 53 (1996), 321-329. Zbl0859.47030
  16. [16] A. Lunardi, On the Ornstein-Uhlenbeck operator in L 2 spaces with respect to invariant measures, Trans. Amer. Math. Soc. 349 (1997), 155-169. Zbl0890.35030
  17. [17] A. Lunardi and V. Vespri, Optimal L 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. [18] A. Lunardi and V. Vespri, Generation of strongly continuous semigroups by elliptic operators with unbounded coefficients in L p ( n ) , Rend. Mat., volume in honour of P. Grisvard, to appear. Zbl0899.35027
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