scholarly journals On the Interior Regularity of Weak Solutions to Nonlinear Elliptic Systems of Second Order

1990 ◽  
Vol 9 (6) ◽  
pp. 535-544 ◽  
Author(s):  
Josef Daněček
Keyword(s):  
Weak Solutions ◽  
Elliptic Systems ◽  
Second Order ◽  
Nonlinear Elliptic Systems ◽  
Nonlinear Elliptic ◽  
Interior Regularity ◽  
Regularity Of Weak Solutions

scholarly journals On the regularity up to the boundary for second order nonlinear elliptic systems

1982 ◽  
Vol 99 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Mariano Giaquinta ◽  
Jindrich Necas ◽  
O. John ◽  
J. Stará
Keyword(s):  
Elliptic Systems ◽  
Second Order ◽  
Nonlinear Elliptic Systems ◽  
Nonlinear Elliptic

A pointwise differential inequality and second-order regularity for nonlinear elliptic systems

2021 ◽  
Author(s):  
Anna Kh. Balci ◽  
Andrea Cianchi ◽  
Lars Diening ◽  
Vladimir Maz’ya
Keyword(s):  
Differential Inequality ◽  
Differential Operators ◽  
Elliptic Systems ◽  
Second Order ◽  
Nonlinear Elliptic Systems ◽  
Nonlinear Elliptic ◽  
Regularity Properties ◽  
Partial Differential Operators ◽  
Global Estimates ◽  
Special Case

AbstractA sharp pointwise differential inequality for vectorial second-order partial differential operators, with Uhlenbeck structure, is offered. As a consequence, optimal second-order regularity properties of solutions to nonlinear elliptic systems in domains in $${\mathbb R^n}$$ R n are derived. Both local and global estimates are established. Minimal assumptions on the boundary of the domain are required for the latter. In the special case of the p-Laplace system, our conclusions broaden the range of the admissible values of the exponent p previously known.

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