Logarithmic Sobolev inequality in the variable exponent setting and its applications to hyperbolic differential equations with a logarithmic source term
DOI:
https://doi.org/10.24193/subbmath.2026.1.08Keywords:
Hyperbolic problem, logarithmic nonlinearity, variational functional, variable exponential Lebesgue space, variable Laplacian, variable Sobolev space, Dirichlet problemAbstract
We establish the generalized parametric logarithmic Sobolev inequalities in the Gagliardo-Nirenberg form for variable exponential space with log Holder exponential function. Employing the generalized parametric logarithmic Sobolev inequalities, we establish the existence of weak solutions to the boundary problem for the hyperbolic equation with logarithmic nonlinearity and involving variable exponents. Numerical examples and further applications will be addressed in a forthcoming paper.
Mathematics Subject Classification (2010): 35J60, 35B30, 35B40, 35L86, 35J05.
Received 30 October 2025; Accepted 03 February 2026.
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