Well-posedness of Tricomi–Gellerstedt–Keldysh-type fractional elliptic problems

We study Tricomi–Gellerstedt–Keldysh-type fractional elliptic equations and obtain results on the well-posedness of fractional elliptic boundary value problems for general positive operators with discrete spectrum and for Fourier multipliers with positive symbols. As examples, we discuss results in half-cylinder, star-shaped graph, half-space and other domains.