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- Tatiana V. Savina, Alexander A. Golovin, S. H. Davis, Alexander A. Nepomnyashchy, Peter W. Voorhees
- Physical review. E, Statistical, nonlinear, and…
- 2003

Consider faceting of a crystal surface caused by strongly anisotropic surface tension, driven by surface diffusion and accompanied by deposition (etching) due to fluxes normal to the surface.… (More)

A non-local reflection formula for harmonic functions in R2 satisfying the Robin boundary condition, α∂nu+βu=0, on a real-analytic curve is suggested. This formula generalizes the celebrated Schwarz… (More)

- Valentyna Orlova, Tatiana V. Savina, +8 authors Nataliya S Demikova
- 2004

The biharmonic equation arises in areas of continuum mechanics including linear elasticity theory and the Stokes flows, as well as in a radar imaging problem. We discuss the reflection formulas for… (More)

A reflection formula is proposed for the case of the Helmholtz equation on a plane. This formula, unlike the classical Schwarz symmetry principle, exhibits a nonlocal (or integral) character

A reflection formula for polyharmonic functions in is suggested. The obtained formula generalizes the celebrated Schwarz reflection principle for harmonic functions to polyharmonic functions. We also… (More)

A mechanism for the formation of quantum dots on the surface of thin solid films is proposed, not associated with the Asaro-Tiller-Grinfeld instability caused by epitaxial stresses. This mechanism,… (More)

A minimal element, mother body, for a family of bodies producing the same external gravitational field is the body in the family, whose support has Lebesgue measure zero and satisfies some additional… (More)

It is well-known that in the framework of the internal Hele-Shaw problem the fluid cannot be fully removed through a single point sink because of a cusp formation occurring prior to the moving… (More)

According to the Schwarz symmetry principle, every harmonic function vanishing on a real-analytic curve has an odd continuation, while a harmonic function satisfying homogeneous Neumann condition has… (More)