QUASI-LINEAR EVOLUTION AND ELLIPTIC EQUATIONS
Abstract
In this article we use a new type of nonlinear elliptic operators that are associated with left side of elliptic equation and studied their properties. We draw up the form, that is associated with non-linear elliptic operator , studying the properties this operator by means of form.
We proved some a priori estimates which are theorems about properties of solutions under certain conditions on the function that forming this equation. We proved the existence of solution of quasi-linear evolution equation with singular coefficients in space by Galerkin method and showed that a given equationhas a solution in the Sobolev space.
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