4 papers
The Lavrentiev phenomenon in calculus of variations with differential forms
Anna Kh. Balci, Mikhail Surnachev
In this article we study convex non-autonomous variational problems with differential forms and corresponding function spaces. We introduce a general framework for constructing cou…
Lavrentiev gap for some classes of generalized Orlicz functions
Anna Kh. Balci, Mikhail Surnachev
In the present paper we find optimal conditions separating the regular case from the one with Lavrentiev gap for the borderline case of double phase potencial and related general c…
New Examples on Lavrentiev Gap Using Fractals
Anna Kh. Balci, Lars Diening, Mikhail Surnachev
Zhikov showed 1986 with his famous checkerboard example that functionals with variable exponents can have a Lavrentiev gap. For this example it was crucial that the exponent had a…
On the uniqueness of a solution to a stationary convection-diffusion equation with a generalized divergence-free drift
Mikhail Surnachev
In this paper we establish the uniqueness of a solution to a stationary convection-diffusion equation in divergence form with an exponentially summable generalized divergence-free…