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The present paper is devoted to the study of the Dirichlet problem${\rm{Re}}\,\omega(z)\to\varphi(\zeta)$ as $z\to\zeta,$ $z\in D,\zeta\in\partial D,$ with continuous boundary data $\varphi :\partial D\to\mathbb R$for Beltrami equations $\omega_{\bar{z}}=\mu(z) \omega_z+\sigma (z)$,$|\mu(z)|<1$ a.e., with sources $\sigma :D\to\mathbb C$ in the case of locallyuniform ellipticity. In this case, we establish a series of effective integralcriteria of the type of BMO, FMO, Calderon-Zygmund, Lehto and Orlicz onsingularities of the equations at the boundary for existence, representationand regularity of solutions in arbitrary bounded domains $D$ of the complexplane $\mathbb C$ with no boun\-da\-ry component degenerated to a single pointfor sources $\sigma$ in $L_p(D)$, $p>2$, with compact support in $D$. Moreover,we prove in such domains existence, representation and regularity of weaksolutions of the Dirichlet problem for the Poisson type equation ${\rm div}[A(z)\nabla\,u(z)] = g(z)$ whose source $g\in L_p(D)$, $p>1$, has compactsupport in $D$ and whose mat\-rix valued coefficient $A(z)$ guarantees itslocally uniform ellipticity.

On Dirichlet problem for degenerate Beltrami equations with sources