ESTIMATE FOR THE GRADIENT OF THE SOLUTION TO THE NEUMANN PROBLEM FOR (p,q)-NONLINEAR EQUATIONS

摘要

We consider the Neumann boundary value problem for the class of (p,q)-nonlinear elliptic equations. The numbers p and q, 2 ≤ p < q, characterize the power growth with respect to the gradient of eigenvalues of the leading matrix of the equation. An a priori estimate for the maximum of the modulus of the gradient of the solution is obtained in a neighborhood of the boundary of the domain for some interval of p and q.