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VIDEO LIBRARY |
Conference on the Theory of Functions of Several Real Variables, dedicated to the 90th anniversary of O. V. Besov
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Dual Morrey spaces in nonlinear elliptic PDEs E. A. Kalita Institute of Applied Mathematics and Mechanics, Donetsk |
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Abstract: We will talk on the following results: For nonlinear elliptic equations and systems with a Hilbert energy space, we establish the solvability in dual Morrey spaces on an interval of scale that explicitly depends on the modulus of ellipticity (in the case of second-order systems, the dependence is exact). This gives the existence of solutions for a wider class of right-hand sides than previously known, e.g. from the Lebesgue spaces with an exponent weaker than the Sobolev exponent, or from Hardy classes for a certain interval For nonlinear elliptic equations and systems with non-Hilbert energy space ( For linear elliptic equations and systems with discontinuous coefficients, we establish the existence of higher-order derivatives of solution; the increase of order depends explicitly on the modulus of ellipticity. The coefficients are assumed to be in the dual Morrey spaces with Lebesgue exponent infinity. They can have e.g. a dense set of discontinuities of type |