The Minty-Browder theorem for nonlinear elliptic equations involving p-Laplacian with singular coefficients under form boundary conditions
DOI:
https://doi.org/10.24193/subbmath.2025.3.10Keywords:
Minty-Browder theorem, regular solution, elliptic equation, nonlinear equation, nonstandard growth, form-boundary, singular coefficientAbstract
We consider the elliptic parabolic partial differential equation with singular coefficients under the rather general form boundary conditions. We proved that the bounded operator associated with the elliptic equation satisfies monotony, coercivity, and semicontinuity conditions. Employing Minty-Browder arguments, we establish the existence and uniqueness of the weak solution to the elliptic equation with singular coefficients under form-boundary conditions.
Mathematics Subject Classification (2010): 35B65, 35K51, 35K61, 35K55.
Received 31 December 2024; Accepted 01 April 2025.
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