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Boundary singularities of solutions to quasilinear elliptic equations

Vladimir Kozlov;  Vladimir Maz'ya — 1999

Journées équations aux dérivées partielles

Asymptotic formulae for solutions to boundary value problems for linear and quasilinear elliptic equations and systems near a boundary point are discussed. The boundary is not necessarily smooth. The main ingredient of the proof is a spectral splitting and reduction of the original problem to a finite-dimensional dynamical system. The linear version of the corresponding abstract asymptotic theory is presented in our new book “Differential equations with operator coefficients”, Springer, 1999.

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

Vladimir Kozlov;  Vladimir Maz'ya — 2003

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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.

On «power-logarithmic» solutions of the Dirichlet problem for elliptic systems in K d × R n - d , where K d is a d-dimensional cone

Vladimir A. Kozlov;  Vladimir G. Maz'ya — 1996

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A description of all «power-logarithmic» solutions to the homogeneous Dirichlet problem for strongly elliptic systems in a n -dimensional cone K = K d × R n - d is given, where K d is an arbitrary open cone in R d and n > d > 1 .

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