November 20, 2018, at 16.30 the seminar on nonlinear problems of PDE and mathematical physics will take place.
Speaker: Doctor of phys.-math. sciences M. Surnachev (Keldysh Institute of Applied Mathematics RAS):
Topic: Regularity of p(x)-harmonic functions without global logarithmic condition.
In this talk continuity of p(x)-harmonic functions will be discussed. By now the qualitative theory of equations with p(x)-Laplacian and properties of corresponding functional spaces are well understood in the case of the exponent p(x) satisfying Zhikov's logarithmic condition. If this condition is not satisfied much less is known. In this talk, the speaker will present recent results on the interior and boundary continuity of p(x)-harmonic function in the case when the global logarithmic condition is absent. We assume only the continuity of p(x) at the given point. The speaker will discuss the regularity of a boundary point and a problem with two-phase p(x)-Laplacian.