Differential and Integral Equations

Schauder estimates for degenerate elliptic and parabolic problems with unbounded coefficients in ${\Bbb R}^N$

Luca Lorenzi

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Abstract

We consider a class of second-order degenerate elliptic operators. Continuing the study started in [3], we prove Schauder estimates for the distributional solutions of the nonhomogeneous elliptic equation $\lambda u-{\mathcal A}u=f$ and the Cauchy problem $D_tu={\mathcal A}u+g$, $u(0,\cdot)=f$.

Article information

Source
Differential Integral Equations, Volume 18, Number 5 (2005), 531-566.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060184

Mathematical Reviews number (MathSciNet)
MR2136978

Zentralblatt MATH identifier
1212.35255

Subjects
Primary: 35K65: Degenerate parabolic equations
Secondary: 35B65: Smoothness and regularity of solutions 35K15: Initial value problems for second-order parabolic equations 35L70: Nonlinear second-order hyperbolic equations

Citation

Lorenzi, Luca. Schauder estimates for degenerate elliptic and parabolic problems with unbounded coefficients in ${\Bbb R}^N$. Differential Integral Equations 18 (2005), no. 5, 531--566. https://projecteuclid.org/euclid.die/1356060184


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