Abstract:
We consider nonlinear elliptic equations and systems of the form $div^t A(x,D^s u)=f(x)$ under structure conditions provide coerciveness and monotonicity in pair with degree of Laplacian $\Delta^{(s-t)/2}u$. For equations and systems of strictly divergent form ($s=t$) the solution depends correctly from right-hand side in some neighborhood of natural energy space. The neighborhood could become arbitrary small under growth of the modulus of ellipticity.
We establish that for $s\ne t$ the neighborhood do not vanish under degeneration of structure condition. We will discuss consequent results including existence and uniqueness of solution under degeneration of coerciveness.