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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
##### Keywords:
Lopatinskij-Shapiro conditions; approximate solutions
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