Advances in Differential Equations

Global summability for solutions to some anisotropic elliptic systems

Francesco Leonetti and Pier Vincenzo Petricca

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We consider the system of $N$ partial differential equations $$ \sum\limits_{i=1}^{n} D_i (a_i^\alpha (x,Du(x))) = 0, \quad x \in \Omega, \quad \alpha \in \{1,...,N\}, $$ and the boundary condition $$ u(x) = u_*(x), \quad x \in \partial\Omega. $$ We show that higher integrability of the boundary datum $u_*$ forces solutions $u$ to have higher integrability as well, provided we assume suitable ellipticity and growth conditions on $a_i^\alpha$.

Article information

Adv. Differential Equations, Volume 20, Number 11/12 (2015), 1165-1186.

First available in Project Euclid: 18 August 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations 35D30: Weak solutions 35J25: Boundary value problems for second-order elliptic equations 49N60: Regularity of solutions


Leonetti, Francesco; Petricca, Pier Vincenzo. Global summability for solutions to some anisotropic elliptic systems. Adv. Differential Equations 20 (2015), no. 11/12, 1165--1186.

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