On the barotropic motion of compressible perfect fluids

H. Beirão Da Veiga

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Boundary-value problems for a class of first order partial differential equations in Sobolev spaces and applications to the Euler flow

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Asymptotic formula for solutions to the Dirichlet problem for elliptic equations with discontinuous coefficients near the boundary

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We derive an asymptotic formula of a new type for variational solutions of the Dirichlet problem for elliptic equations of arbitrary order. The only a priori assumption on the coefficients of the principal part of the equation is the smallness of the local oscillation near the point.