Global boundedness for Generalized Schrödinger-Type Double Phase Problems in $\mathbb{R}^N$ and Applications to Supercritical Double Phase Problems
Year: 2025
Type: preprint
Abstract: We establish two global boundedness results for weak solutions to generalized Schrödinger-type double phase problems with variable exponents in $\mathbb{R}^N$ under new critical growth conditions optimally introduced in [26, 32]. More precisely, for the case of subcritical growth, we employ the De Giorgi iteration with a suitable localization method in $\mathbb{R}^N$ to obtain a-priori bounds. As a byproduct, we derive the decay property of weak solutions. For the case of critical growth, using the De Giorgi iteration with a localization adapted to the critical growth, we prove the global boundedness. As an interesting application of these results, the existence of weak solutions for supercritical double phase problems is shown. These results are new even for problems with constant exponents in $\mathbb{R}^N$.
Source: arXiv (Cornell University)
Authors: Ha, Hoang Hai, Ho, Ky, Quan, Bui The, Sim, Inbo
Institution: University of Ulsan
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4820969610
OpenAlex ID: W6979322259
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