scholarly journals Existence, uniqueness and optimal regularity results for very weak solutions to nonlinear elliptic systems

2016 ◽  
Vol 9 (5) ◽  
pp. 1115-1151 ◽  
Author(s):  
Miroslav Bulíček ◽  
Lars Diening ◽  
Sebastian Schwarzacher
Keyword(s):  
Weak Solutions ◽  
Elliptic Systems ◽  
Very Weak Solutions ◽  
Nonlinear Elliptic Systems ◽  
Optimal Regularity ◽  
Nonlinear Elliptic ◽  
Regularity Results

On the regularity of very weak minima

1996 ◽  
Vol 126 (2) ◽  
pp. 287-296 ◽  
Author(s):  
Daniela Giachetti ◽  
Francesco Leonetti ◽  
Rosanna Schianchi
Keyword(s):  
Weak Solutions ◽  
Elliptic Systems ◽  
Very Weak Solutions ◽  
Nonlinear Elliptic Systems ◽  
Higher Integrability ◽  
Nonlinear Elliptic ◽  
Variational Integrals ◽  
Weak Minima

We consider very weak minimisers u of variational integrals ∫ F(x, Du(x)) dx and very weak solutions u of nonlinear elliptic systems div A(x, u, Du) = 0; we prove higher integrability for the gradient Du without any homogeneity on ξ→A(x,u,ξ) thus improving on a result by Iwaniec and Sbordone.

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