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Viscosity Solutions for First-Order PDEs With Measurable Coefficients and Superlinear Gradient Growth

Author

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  • S. M. E. Hosseini
  • S. S. Nezhad

Abstract

Inspired by a fundamental existence result in the theory of PDEs, we present a general existence theorem for viscosity solutions in the standard sense that is applicable to a wide class of partial differential equations. These equations are characterized by coefficients that are merely measurable, with no continuity assumptions imposed. To illustrate the scope and flexibility of the main result, we derive several propositions for specific families of PDEs, including examples that fall outside the reach of prior existence theorems with stronger regularity hypotheses.

Suggested Citation

  • S. M. E. Hosseini & S. S. Nezhad, 2026. "Viscosity Solutions for First-Order PDEs With Measurable Coefficients and Superlinear Gradient Growth," Journal of Mathematics, Hindawi, vol. 2026, pages 1-8, June.
    • Handle: RePEc:hin:jjmath:6026158
    DOI: 10.1155/jom/6026158
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