Frank Duzaar

Parabolic Systems with Polynomial Growth and Regularity

The authors establish a series of optimal regularity results for solutions to general non-linear parabolic systems

Degenerate problems with irregular obstacles

u_t- \mathrm{div} \ a(x,t,u,Du)+H=0,

Local Lipschitz regularity for degenerate elliptic systems

under the main assumption of polynomial growth at rate

PARTIAL REGULARITY FOR ALMOST MINIMIZERS OF QUASI-CONVEX INTEGRALS ∗

p

The existence of regular boundary points for non-linear elliptic systems

i.e.

Elliptic Systems, Singular Sets and Dini Continuity

|a(x,t,u,Du)|\leq L(1+|Du|^{p-1}), p \geq 2.

Higher integrability for parabolic systems with non-standard growth and degenerate diffusions

They give a unified treatment of various interconnected aspects of the regularity theory: optimal partial regularity results for the spatial gradient of solutions, the first estimates on the (parabolic) Hausdorff dimension of the related singular set, and the first Calderon-Zygmund estimates for non-homogeneous problems are achieved here.

Regularity of ω-minimizers of quasi-convex variational integrals with polynomial growth

Abstract We establish the natural Calderón and Zygmund theory for solutions of elliptic and parabolic obstacle problems involving possibly degenerate operators in divergence form of p-Laplacian type, and proving that the (spatial) gradient of solutions is as integrable as that of the assigned obstacles. We also include an existence and regularity theorem where obstacles are not necessarily considered to be non-increasing in time.

Porous Medium Type Equations with Measure Data and Potential Estimates

We start presenting an

Gradient estimates in non-linear potential theory

L^{\infty}