A. G. Ramm

activity

20012023

most citedAn inverse problem for a heat equation with piecewise-constant thermal conductivity

8 citations · 12 across the 15 of their papers we have counts for

collaborators

15 papers

math.CV2023

Boundary values of analytic functions

Alexander G. Ramm

Let $D$ be a connected bounded domain in $R^{2}$ , $S$ be its boundary which is closed, connected and smooth. Let $Φ (z) = \frac{1}{2 π i} \int_{S} \frac{f ( s ) d s}{s - z}$ , $f \in L^{1} (S)$ , $z=x+iy…

math.AP2017

Proof of the Schiffer's conjecture

A. G. Ramm

The following conjecture has been known for many decades as Schiffer's symmetry problem (or Schiffer's conjecture): Assume that $Δ u + k^{2} u = 0$ in $D$ , $u ∣_{S} = 0$ , $u_{N} ∣_{S} = 1$ , where $D\s…

math.AP2015

A symmetry result for strictly convex domains

A. G. Ramm

Assume that $D \subset R^{2}$ is a strictly convex domain with $C^{2} -$ smooth boundary. {\bf Theorem.} {\em If $\int_{D} e^{i x} y^{n} d x d y = 0$ for all sufficiently large $n$ , then $D$ is a dis…

math-ph2014

Symmetry problem

Alexander G. Ramm

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

math-ph2012★ 1 cited

Many-body wave scattering problems in the case of small scatterers

A. G. Ramm

Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogen…

math.NA2011

A collocation method for solving some integral equations in distributions

Sapto W. Indratno, Alexander G. Ramm

A collocation method is presented for numerical solution of a typical integral equation Rh :=\int_D R(x, y)h(y)dy = f(x), x ε D of the class R, whose kernels are of positive ration…