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<p>First, we establish some extended and refined results in the theory of viscosity solutions including a continuous dependence theorem, and a regularity result. Then, by investigating a certain type of partial differential equations, we expand the application of viscosity solutions to a broad range of higher-order partial differential equations. Finally, in the last section, we prove some corollaries that show the applicability of our results.</p>

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New Insights in the Application of Viscosity Solutions for Some Higher-Order Partial Differential Equations

  • 期刊论文

  • 发表日期：

    2025年4月1日

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

摘要

First, we establish some extended and refined results in the theory of viscosity solutions including a continuous dependence theorem, and a regularity result. Then, by investigating a certain type of partial differential equations, we expand the application of viscosity solutions to a broad range of higher-order partial differential equations. Finally, in the last section, we prove some corollaries that show the applicability of our results.