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A construction of parametrices of elliptic boundary value problems. (English) Zbl 0826.35032
The authors study the regularity for problems \[ Pu = f \text{ in } \Omega \subset \mathbb{R}^{n + 1}, \quad D^p_y u = g_p,\;p = \overline {0,m - 1} \text{ in } \partial \Omega, \tag{1} \] where \(\Omega\) is smooth and the operator \(P\) is of order \(2m\), linear with smooth coefficients and properly elliptic. There are \(m\) boundary conditions and the Lopatinskij-Shapiro conditions are assumed to be verified. A new way of obtaining approximate solutions of problem (1) is presented. Solutions are expressed by means of parametrices.
MSC:
35J40 Boundary value problems for higher-order elliptic equations
35D10 Regularity of generalized solutions of PDE (MSC2000)
35S15 Boundary value problems for PDEs with pseudodifferential operators
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