scholarly journals Higher Integrability for Very Weak Solutions of InhomogeneousA-Harmonic Form Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Yuxia Tong ◽  
Shenzhou Zheng ◽  
Jiantao Gu
Keyword(s):  
Weak Solutions ◽  
Harmonic Form ◽  
Very Weak Solutions ◽  
Higher Integrability

The higher integrability for very weak solutions ofA-harmonic form equationsd*A(x,u,du)=B(x,u,du)has been proved.

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.

scholarly journals Higher Integrability of Weak Solutions to a Class of Double Obstacle Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhenhua Hu ◽  
Shuqing Zhou
Keyword(s):  
Differential Equation ◽  
Weak Solutions ◽  
Second Order ◽  
Obstacle Problems ◽  
Elliptic Differential Equation ◽  
Higher Integrability ◽  
Global Higher Integrability ◽  
Quasilinear Elliptic

We first introduce double obstacle systems associated with the second-order quasilinear elliptic differential equationdiv(A(x,∇u))=div f(x,u), whereA(x,∇u),f(x,u)are twon×Nmatrices satisfying certain conditions presented in the context, then investigate the local and global higher integrability of weak solutions to the double obstacle systems, and finally generalize the results of the double obstacle problems to the double obstacle systems.

scholarly journals Uniqueness of very weak solutions for a fractional filtration equation

2020 ◽  
Vol 365 ◽  
pp. 107041 ◽  
Author(s):  
Gabriele Grillo ◽  
Matteo Muratori ◽  
Fabio Punzo
Keyword(s):  
Weak Solutions ◽  
Very Weak Solutions ◽  
Filtration Equation

scholarly journals Very weak solutions to hypoelliptic wave equations

2020 ◽  
Vol 268 (5) ◽  
pp. 2063-2088
Author(s):  
Michael Ruzhansky ◽  
Nurgissa Yessirkegenov
Keyword(s):  
Weak Solutions ◽  
Wave Equations ◽  
Very Weak Solutions
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