- Publications
- Influence

Claim Your Author Page

Ensure your research is discoverable on Semantic Scholar. Claiming your author page allows you to personalize the information displayed and manage publications.

The regularity theory of free boundaries flourished during the late 1970s and early 1980s and had a major impact in several areas of mathematics, mathematical physics, and industrial mathematics, as… (More)

For the parabolic obstacle-problem-like equation Delta u - partial derivative(t)u = lambda(+chi{u>0})-lambda(-chi{u 0} boolean OR partial derivative{u < 0} is in a neighborhood of each "branc ...

We consider an evolution which starts as a flow of smooth surfaces in nonparametric form propagating in space with normal speed equal to the mean curvature of the current surface. The boundaries of… (More)

- Henrik Shahgholian, N N Uraltseva, Georg S. Weiss
- 2004

Abstract.Concerning the obstacle-problem-like equation $\Delta u = {\lambda_+\over 2} \chi_{\{u > 0\}}-{\lambda_-\over 2}\chi_{\{u < 0\}}$, where λ+ > 0 and λ− > 0, we give a complete… (More)

- N N Uraltseva
- 1995

Holder estimates of solutions to initial-boundary value problems for parabolic equations of nondivergent form with Wentzel boundary condition by D. E. Apushkinskaya and A. I. Nazarov Reverse Holder… (More)

In the upper half of the unit ball B+ = {\x\ 0}, let u and Omega (a domain in R-+(n) = {X is an element of R-n : x(1) > 0}) solve the following overdetermined problem: Deltau = chi(Omega) in B+, u ...

For the two-phase membrane problem
\Delta u=\lambda_{+}\chi_{\{u>0\}}-\lambda_{-}\chi_{\{u<0\}},
where \lambda_{+} and \lambda_{-} are positive Lipschitz functions, we prove in higher dimensions… (More)

- D E Apushkinskaya, N N Uraltseva
- Philosophical transactions. Series A…
- 2015

Here, we present a survey concerning parabolic free boundary problems involving a discontinuous hysteresis operator. Such problems describe biological and chemical processes 'with memory' in which… (More)

We consider equations with the simplest hysteresis operator at the right-hand side. Such equations describe the so-called processes "with memory" in which various substances interact according to the… (More)