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.
Giusti,Direct Methods in the Calculus of Variations, World Scientific Publishing Co
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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.