Schauder estimates for degenerate Lévy Ornstein-Uhlenbeck operators

2021 ◽  
Vol 500 (1) ◽  
pp. 125168
Author(s):  
Lorenzo Marino
Keyword(s):  
Schauder Estimates

scholarly journals Nonlinear Beltrami operators, Schauder estimates and bounds for the Jacobian

2017 ◽  
Vol 34 (6) ◽  
pp. 1543-1559 ◽  
Author(s):  
Kari Astala ◽  
Albert Clop ◽  
Daniel Faraco ◽  
Jarmo Jääskeläinen ◽  
Aleksis Koski
Keyword(s):  
Schauder Estimates

scholarly journals Global Schauder Estimates for the $$\mathbf {p}$$-Laplace System

2021 ◽  
Author(s):  
D. Breit ◽  
A. Cianchi ◽  
L. Diening ◽  
S. Schwarzacher
Keyword(s):  
Global Regularity ◽  
Regularity Theory ◽  
Divergence Form ◽  
Dirichlet Problems ◽  
Schauder Estimates ◽  
First Order ◽  
Right Hand ◽  
Regularity Results ◽  
The Right ◽  
Linear Setting

AbstractAn optimal first-order global regularity theory, in spaces of functions defined in terms of oscillations, is established for solutions to Dirichlet problems for the p-Laplace equation and system, with the right-hand side in divergence form. The exact mutual dependence among the regularity of the solution, of the datum on the right-hand side, and of the boundary of the domain in these spaces is exhibited. A comprehensive formulation of our results is given in terms of Campanato seminorms. New regularity results in customary function spaces, such as Hölder, $$\text {BMO}$$ BMO and $${{\,\mathrm{VMO}\,}}$$ VMO spaces, follow as a consequence. Importantly, the conclusions are new even in the linear case when $$p=2$$ p = 2 , and hence the differential operator is the plain Laplacian. Yet in this classical linear setting, our contribution completes and augments the celebrated Schauder theory in Hölder spaces. A distinctive trait of our results is their sharpness, which is demonstrated by a family of apropos examples.

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