Partial Schauder Estimates for Second-Order Elliptic and Parabolic Equations: A Revisit
نویسندگان
چکیده
منابع مشابه
Schauder Estimates for Elliptic and Parabolic Equations
The Schauder estimate for the Laplace equation was traditionally built upon the Newton potential theory. Different proofs were found later by Campanato [Ca], in which he introduced the Campanato space; Peetre [P], who used the convolution of functions; Trudinger [T], who used the mollification of functions; and Simon [Si], who used a blowup argument. Also a perturbation argument was found by Sa...
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We consider a class of second order elliptic operators on a d-dimensional cube Sd . We prove that if the coefficients are of class Ck+δ(Sd ), with k = 0,1 and δ ∈ (0,1), then the corresponding elliptic problem admits a unique solution u belonging to Ck+2+δ(Sd) and satisfying non-standard boundary conditions involving only second order derivatives. 2003 Éditions scientifiques et médicales Else...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2017
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnx180