Anna Kh.Balci

I am mathematician working on

analysis and numerics for partial differential equations.

Starting from October 2023 I am tenure track Assistant Professor

Charles University in Prague, Czech Republic .

I am principal investigator of the project Differential and integro-differential operators with degenerate coefficients as the part of

CRC 1283: Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications at the University Bielefeld, Germany.

Before this I was the DAAD fellow at the University Bielefeld and lecturer(Docent) at the Financial University in Moscow, Russia.

I obtained PhD degree in mathematics in 2014 supervised by Prof. Svetlana Pastukhova and Prof. Vasilii Zhikov at Vladimir State University, Russia.

Married and mother of one daughter, Mira

My research is available here:

Orcid ID: 0000-0002-8138-9067

Get in touch at akhripun at math.uni-bielefeld dot de

News

Minisymposia

ICIAM 2023 Tokyo – The 10th ICIAM in Tokyo, Japan

Nonlinear and nonlocal models: analysis and numerics

iciam2023.org/

The paper "Finite element method for non-autonomous variational problems with Lavrentiev gap" is published

Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap - Numerische MathematikWe investigate the convergence of the Crouzeix-Raviart finite element method for variational problems with non-autonomous integrands that exhibit non-standard growth conditions. While conforming schemes fail due to the Lavrentiev gap phenomenon, we prove that the solution of the Crouzeix-Raviart scheme converges to a global minimiser. Numerical experiments illustrate the performance of the scheme and give additional analytical insights.

The paper "Elliptic Equations with Degenerate Weights is published"

Elliptic Equations with Degenerate Weights | SIAM Journal on Mathematical AnalysisWe obtain new local Calderón--Zygmund estimates for elliptic equations with matrix-valued weights for linear as well as nonlinear equations. We introduce a novel log-BMO condition on the weight $\mathbb M$. In particular, we assume smallness of the logarithm of the matrix-valued weight in BMO. This allows us to include degenerate, discontinuous weights. The assumption on the smallness parameter is sharp and linear in terms of the integrability exponent of the gradient. This is a novelty even in the linear setting with nondegenerate weights compared to previously known results, where the dependency was exponential. We provide examples that show the sharpness of the estimates in terms of the log-BMO norm.