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- W4380551434 abstract "The paper is devoted to the study of the Dirichlet problem ${rm{Re}},omega(z)tovarphi(zeta)$ as $ztozeta,$ $zin D,zetain partial D,$ with continuous boundary data $varphi :partial Dtomathbb R$ for Beltrami equations $omega_{bar{z}}=mu(z) omega_z+sigma (z)$, $|mu(z)|<1$ a.e., with sources $sigma :Dtomathbb C$ in the case of locally uniform ellipticity. In this case, we have established a series of effective integral criteria of the BMO, FMO, Calderon-Zygmund, Lehto, and Orlicz types on the singularities of the equations at the boundary for the existence, representation, and regularity of solutions in arbitrary bounded domains $D$ of the complex plane $mathbb C$ with no boun-da-ry component degenerated to a single point for sources $sigma$ in $L_p(D)$, $p>2$, with compact support in $D$. Moreover, we have proved the existence, representation, and regularity of weak solutions of the Dirichlet problem in such domains for the Poisson-type equation ${rm div} [A(z)nabla,u(z)] = g(z)$, whose source $gin L_p(D)$, $p>1$, has compact support in $D$ and whose mat-rix-valued coefficient $A(z)$ guarantees its locally uniform ellipticity." @default.
- W4380551434 created "2023-06-14" @default.
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- W4380551434 date "2023-03-28" @default.
- W4380551434 modified "2023-10-18" @default.
- W4380551434 title "The Dirichlet problem for the Beltrami equations with sources" @default.
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- W4380551434 doi "https://doi.org/10.37069/1810-3200-2023-20-1-2" @default.
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