Regularity for quasi-linear elliptic systems with discontinuous coefficients

A maximum principle for linear elliptic systems with discontinuous coefficients

We prove a maximum principle for linear second order elliptic systems in divergence form with discontinuous coefficients under a suitable condition on the dispersion of the eigenvalues of the coefficients matrix.

Viscous approach for Linear Hyperbolic Systems with Discontinuous Coefficients

— We introduce small viscosity solutions of hyperbolic systems with discontinuous coefficients accross the fixed noncharacteristic hypersurface {xd = 0}. Under a geometric stability assumption, our first result is obtained, in the multi-D framework, for piecewise smooth coefficients. For our second result, the considered operator is ∂t+a(x)∂x, with sign(xa(x)) > 0 (expansive case not included i...

Elliptic regularity and solvability for PDEs with Colombeau coefficients

The paper addresses questions of existence and regularity of solutions to linear partial differential equations whose coefficients are generalized functions or generalized constants in the sense of Colombeau. We introduce various new notions of ellipticity and hypoellipticity, study their interrelation, and give a number of new examples and counterexamples. Using the concept of G∞-regularity of...

L^p-Regularity for Elliptic Operators with Unbounded Coefficients

Boundary regularity for elliptic problems with continuous coefficients

We consider weak solutions of second order nonlinear elliptic systems in divergence form or of quasi-convex variational integrals with continuous coefficients under superquadratic growth conditions. Via the method of A-harmonic approximation we give a characterization of regular boundary points using and extending some new techniques recently developed by M. Foss & G. Mingione in [15].