Abstract
The present paper studies the Dirichlet problem for elliptic equations degenerate on part of the boundary of a domain and the degeneracy is of the Keldysh type. By introducing a proper metric that is related to the operator we establish the global Hölder estimates when some well-posed boundary conditions are satisfied. The main methods are the construction of some barrier functions and the interpolation of the estimates of uniformly elliptic operators.
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Song, Q., Wang, L. Hölder estimates for elliptic equations degenerate on part of the boundary of a domain. manuscripta math. 139, 179–200 (2012). https://doi.org/10.1007/s00229-011-0512-3
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DOI: https://doi.org/10.1007/s00229-011-0512-3