[PDF] Top 20 Global L∞ gradient estimates for solutions to a certain degenerate elliptic equation

... to a function u: this in general will not be a minimizer of the original problem, due to the lack of ...converge, to a limit stress field of the form ∇H ∗ (∇u 0 ), with u 0 ... Voir le document complet

... nonlinear elliptic and parabolic equations, obtaining local or global gradient bounds is often a key step for proving the existence of solutions but it may be even more useful in ... Voir le document complet

... on a “weighted” norm of ∇u x j , where the weights depend on all the other components u x i of the gradient, through the nonlinear functions (h ∗ i ) ′′ ...inequality for these weighted integrals. ... Voir le document complet

... method for constructing solutions of nonlinear evolution ...advantage to require less regularity on the initial data, one allows infinite energy while the Leray method requires finite energy of the ... Voir le document complet

... superlinear gradient term. Like in the pioneering paper of Brezis for the semilinear case, we obtain the existence of entire viscosity solutions, defined in all the space, without assuming ... Voir le document complet

... A Gradient scheme for the discretization of Richards Equation Konstantin Brenner, Danielle Hilhorst, Huy Cuong Vu Do Abstract We propose a finite volume method on general meshes ... Voir le document complet

... thanks to a special first integral of motion for the charac- teristics system associated with ...weak solutions not at the level of measures on the phase space but on a (possibly ... Voir le document complet

... corresponding degenerate inhomoge- neous problem divA∇u = f, with divA∇u denoting the left hand side in ( 1 ...). A study of such equations would be of interest in its own right, but could also prove useful ... Voir le document complet

... with elliptic estimates to control the fluid part by the mi- croscopic part in Sobolev spaces H s ...contribution to avoid involving high regularity is based on an adaptation of the recent ... Voir le document complet

... is a natural higher dimensional version of H s {2 1{4 pR t ...condition, a limitation which is lifted here. On the issue of Strichartz estimates, ...on a half space with nonhomogeneous ... Voir le document complet

... weakly degenerate case that is of interest for us here has been totally solved in [6, 1], where some global parabolic Carleman estimates (similar to the ones proved in [13] for ... Voir le document complet

... an elliptic partial dierential equation with random coecients and homogeneous Dirichlet boundary ...of a lognormal coecient, we have then to deal with the lack of uniform coercivity and ... Voir le document complet

... corresponding to a quasi-linear elliptic equation in a 2-dimensional convex do- ...at a given level, for analytic solutions of fully nonlinear elliptic ... Voir le document complet

... seem to adopt similar rates of convergence for E H 1 ,ζ on hexagonal and locally refined Cartesian meshes; the differences mostly lie in the multiplicative constants, with the largest factor between these ... Voir le document complet

... (1.8) for t > s ≥ 0 and ϑ ∈ C 0 ∞ (R N ...the estimates (1.6), (1.7), and not the existence of a viscosity solution to ...owing to the poor regularity of the solutions ... Voir le document complet

... As a remark, any nondegenerate local minimizer of I 0 is a strict local minimizer, so we recover the main theorem of ...Yamabe equation on the sphere is a strict local ...of a sphere ... Voir le document complet

... exists a critical point of I R which we denote by (u R , v R ), and corresponding to a critical value c R ≥ ...solution for the system (S H p,q R ), ... Voir le document complet

... and degenerate nonlinear diffusion, which arise in the framework of the transport of energy in porous media with thermodynamic transitions, is done using a θ-scheme based on the centred gradient ... Voir le document complet

... Thus, for $t_{0}$ sufficiently large, $ u_{0}=t_{0}^{1/p}¥varphi$ satisfies $||u_{0}||>R_{0}$ and $I_{R}(u_{0})¥leq 0$ ...exists a critical point of $I_{R}$ which we denote by $u_{R}$ , and a ... Voir le document complet

... Pohozaev-Tesei [11]. However the concept of solution used there was stronger; our concept is the weakest possible. We also observe that Theorem 2 seems (formally) to contradict the Implicit Function Theorem since ... Voir le document complet