schauder estimate
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2021 ◽  
Vol 4 ◽  
pp. 369-405
Author(s):  
Cyril Imbert ◽  
Clément Mouhot


2021 ◽  
pp. 2150039
Author(s):  
Xiangao Liu ◽  
Zixuan Liu ◽  
Kui Wang

Motivated by Giaquinta and Hildebrandt’s regularity result for harmonic mappings [M. Giaquinta and S. Hildebrandt, A priori estimates for harmonic mappings, J. Reine Angew. Math. 1982(336) (1982) 124–164, Theorems 3 and 4], we show a [Formula: see text]-regularity result of the harmonic flow between two Riemannian manifolds when the image is in a regular geodesic ball. The proof is based on De Giorgi–Moser’s iteration and Schauder estimate.



2021 ◽  
Vol 14 (1) ◽  
pp. 171-204
Author(s):  
Cyril Imbert ◽  
Luis Silvestre


Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo

This chapter proves existence of solutions to the inhomogeneous problem using the Schauder estimate and analyzes a generalized Kimura diffusion operator, L, defined on a manifold with corners, P. The discussion centers on the solution w = v + u, where v solves the homogeneous Cauchy problem with v(x, 0) = f(x) and u solves the inhomogeneous problem with u(x, 0) = 0. The chapter first provides definitions for the Wright–Fisher–Hölder spaces on a general compact manifold with corners before explaining the steps involved in the existence proof. It then verifies the induction hypothesis and treats the k = 0 case. It also shows how to perform the doubling construction for P and considers the existence of the resolvent operator and a contraction semi-group. Finally, it discusses the problem of higher regularity.



2016 ◽  
Vol 354 (4) ◽  
pp. 371-375 ◽  
Author(s):  
Kai Du ◽  
Jiakun Liu


1991 ◽  
Vol 118 (3-4) ◽  
pp. 193-207 ◽  
Author(s):  
Yousong Luo ◽  
Neil S. Trudinger

SynopsisWe prove a Schauder estimate for solutions of linear second order elliptic equations with linear Venttsel boundary conditions, and establish an existence result for classical solutions for such boundary value problems.



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