Local weak solutions to fully anisotropic widely degenerate parabolic PDEs with measurable (x,t)-dependent coefficients are bounded if in a non-homogeneous De Giorgi class and possess semicontinuous representatives under suitable assumptions on the exponents p_i.
Troisi,Teoremi di inclusione per spazi di Sobolev non isotropi, Ricerche Mat.18, 3-24 (1969)
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Widely degenerate anisotropic diffusion: local boundedness and semicontinuity
Local weak solutions to fully anisotropic widely degenerate parabolic PDEs with measurable (x,t)-dependent coefficients are bounded if in a non-homogeneous De Giorgi class and possess semicontinuous representatives under suitable assumptions on the exponents p_i.