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Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
October 24, 2018 16:00, Moscow, Steklov Mathematical Institute, Room 530 (8 Gubkina)


Nonlinear elliptic equations of nonstrictly divergent form

E. A. Kalita



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.


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