Convexity Properties of the Free Boundary and Gradient Estimates for Quasi-linear Elliptic Equations

Hess, Nonlinear parabolic boundary value problems with upper and lower solutions, Isra.. De La Pradelle, Sur Certaines Perturbations Non Lin´ eaires du

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des

Intuitively, wherever the gradient of a function u is small, the function will be Lipschitz, so we should not need any further information from the equation at those points in order

It is also very useful when we make a systematic analysis of the gradients of solutions of nonlinear elliptic and parabolic problems near the boundary of the irregular domain which

For a general class of autonomous quasi-linear elliptic equations on R n we prove the existence of a least energy solution and show that all least energy solutions do not change

The main applications we have in mind is the study of doubly nonlinear evolution problems of elliptic-parabolic type and degenerate parabolic problems of Stefan or Hele–Shaw type,

Then we give at a formal level the extension of the system (1.8)–(1.9) to dimensions higher than 2. The estimate for the gradient is unchanged but the one on the curvature is

MKRTYCHYAN, An estimate of the solution gradient and the classical solvability of the first initial-boundary value problem for a class of quasilinear