Entire solutions of fully nonlinear elliptic equations with a superlinear gradient term

An alternative approach to find a modulus of continuity for solutions of the rescaled equation (see (6) below) for large slopes could be to apply the Harnack inequality from [15] to

Recall that a solution to a partial differential equation is usually referred to as a singular solution if it satisfies (1.2), the main examples being the so-called

MARCUS, Large solutions of semilinear elliptic equations: existence, uniqueness and asymptotic behavior, Jl. MARCUS, Large solutions of semilinear elliptic equations

PRIGNET, Remarks on existence and uniqueness of solutions of elliptic problems with right-hand side measures, Rend. SERRIN, Pathological solutions of elliptic

The first theorem, Theorem 2.1, is a Harnack inequality for the level sets, the second is an improvement of flatness (Theorem 2.2) and the third theorem gives the equation for

u E need not be a locally integrable function, and that this definition of derivative is not a definition in the sense of distributions5. The following straightforward

Ex = Nx (E being a linear operator with a finite dimensional kernel, the partial inverse g of E being compact, and N nonlinear) and we have already2. shown [4,

Nonlinear elliptic equations, continuity of solutions, lower bounded slope condition, Lavrentiev phenomenon.. 1 Universit´ e Aix-Marseille 1, LATP UMR6632 3 place Victor Hugo,