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arXiv · 2411.03970

Nonexistence results for a degenerate Goursat type Problem

Carlos Alberto Reyes Peña·Olimpio Hiroshi Miyagaki·Rodrigo da Silva Rodrigues
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Abstract

For a generalization of the Gellerstedt operator with Dirichlet boundary conditions in a Tricomi domain. We establish Poho\v{z}aev-type identities and prove the nonexistence of nontrivial regular solutions. Furthermore, we investigate the critical exponent phenomenon for power-type nonlinearities, characterized by the critical exponent of a weighted Sobolev embedding.

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Carlos Alberto Reyes Peña, Olimpio Hiroshi Miyagaki, Rodrigo da Silva Rodrigues. 2024-11-06. Nonexistence results for a degenerate Goursat type Problem. https://arxiv.org/abs/2411.03970

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