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We make use of continuum elasticity theory to investigate the collectivemodes that propagate along the edge of a two-dimensional electron liquid orcrystal in a magnetic field. An exact solution of the equations of motion isobtained with the following simplifying assumptions: (i) The system is {\itmacroscopically} homogeneous and isotropic in the half-plane delimited by theedge (ii) The electron-electron interaction is of finite range due to screeningby external electrodes (iii) The system is nearly incompressible. Atsufficiently small wave vector $q$ we find a universal dispersion curve $\omega\sim q$ independent of the shear modulus. At larger wave vectors the dispersioncan change its form in a manner dependent on the comparison of various lengthscales. We obtain analytical formulas for the dispersion and damping of themodes in various physical regimes.Comment: 3 figure

Continuum elasticity theory of edge waves in a two-dimensional electron liquid with finite-range interactions