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

S. M. E. Hosseini and S. S. Nezhad

Journal of Mathematics, 2026, vol. 2026, 1-8

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.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2026/6026158.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2026/6026158.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6026158

DOI: 10.1155/jom/6026158

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().