28 citations · 58 across the 10 of their papers we have counts for
13 papers
Properties of the phase boundary in the parabolic problem with hysteresis
Darya Apushkinskaya, Sergey Tikhomirov, Nina Uraltseva
We study solutions of parabolic equations with a discontinuous hysteresis operator, described by a free interface boundary. It is established that for spatially transverse initial…
Around the normal derivative lemma
Darya E. Apushkinskaya, Alexander I. Nazarov
This survey provides a description of the history and the state of the art of one of the most important fields in the qualitative theory of elliptic partial differential equations…
Functional a posteriori error estimates for parabolic obstacle problems
Darya E. Apushkinskaya, Sergey I. Repin
The paper is concerned with functional type a posteriori estimates for the initial boundary value problem for a parabolic partial differential equation with an obstacle. We deduce…
Biharmonic obstacle problem: guaranteed and computable error bounds for approximate solutions
Darya E. Apushkinskaya, Sergey I. Repin
The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the differenc…
Venttsel boundary value problems with discontinuous data
Darya E. Apushkinskaya, Alexander I. Nazarov, Dian K. Palagachev +1
We study linear and quasilinear Venttsel boundary value problems involving elliptic operators with discontinuous coefficients. On the base of the a priori estimates obtained, maxim…
In Search of Shadows: the First Topological Conference, Moscow 1935
D. E. Apushkinskaya, A. I. Nazarov, G. I. Sinkevich
We discuss some mistakes and curiosities concerned with the celebrated First International Topological Conference in Moscow, 1935.
On the Boundary Point Principle for divergence-type equations
Darya E. Apushkinskaya, Alexander I. Nazarov
We provide some versions of the Zaremba-Hopf-Oleinik boundary point lemma for general elliptic and parabolic equations in divergence form under the sharp requirements on the coeffi…
Vladimir Ivanovich Smirnov (1887-1974)
Darya E. Apushkinskaya, Alexander I. Nazarov
The year 2017 marked the 130th anniversary of the prominent Russian mathematician Vladimir Ivanovich Smirnov. We review some aspects of his life and his mathematical accomplishment…
Thin obstacle problem: estimates of the distance to the exact solution
Darya E. Apushkinskaya, Sergey I. Repin
We consider elliptic variational inequalities generated by obstacle type problems with thin obstacles. For this class of problems, we deduce estimates of the distance (measured in…
A counterexample to the Hopf-Oleinik lemma (elliptic case)
D. E. Apushkinskaya, A. I. Nazarov
We construct a new counterexample confirming the sharpness of the Dini-type condition for the boundary of . In particular, we show that for convex domains the Dini-type assumpti…
Free boundaries in problems with hysteresis
D. E. Apushkinskaya, N. N. Uraltseva
In this note we present a survey concerning parabolic free boundary problems involving a discontinuous hysteresis operator. Such problems describe biological and chemical processes…
Uniform estimates near the initial state for solutions to the two-phase parabolic problem
D. E. Apushkinskaya, N. N. Uraltseva
This paper is devoted to a proof of optimal regularity, near the initial state, for weak solutions to the two-phase parabolic obstacle problem. The approach used here is general en…
Geometric and Electromagnetic Aspects of Fusion Pore Making
Darya Apushkinskaya, Evgeny Apushkinsky, Bernhelm Booss-Bavnbek +1
For regulated exocytosis, we model the morphology and dynamics of the making of the fusion pore or porosome as a cup-shaped lipoprotein structure (a dimple or pit) on the cytosol s…