What does this research mean for the field?

Under suitable small-aperture assumptions, Calderón-Zygmund type global regularity estimates hold in weighted Lorentz and Morrey-Lorentz spaces for the Hessian of viscosity solutions to non-convex fully nonlinear elliptic equations with oblique boundary conditions. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish global regularity estimates for the Hessian of viscosity solutions to non-convex fully nonlinear elliptic equations with oblique boundary conditions in weighted Lorentz and Morrey-Lorentz spaces.

September 14, 2026Analysis and Applications

Global Lorentz-type regularity for non-convex fully nonlinear elliptic equations with oblique boundary conditions and applications

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Authors

JBJunior da S. BessaUniversidade Estadual de Campinas (UNICAMP)

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Implication

Theoretical analysis demonstrates global Calderón-Zygmund estimates in fully nonlinear elliptic equations with oblique boundaries, indicating broad applicability to obstacle problems.

Key Points

To establish global regularity estimates for the Hessian of viscosity solutions to non-convex fully nonlinear elliptic equations with oblique boundary conditions in weighted Lorentz and Morrey-Lorentz spaces.
Analyzed the ellipticity coefficients of the governing non-convex fully nonlinear operator under small-aperture assumptions.
Applied Calderón-Zygmund type analytical frameworks to evaluate viscosity solutions across weighted Lorentz and Morrey-Lorentz function spaces.
Obtained new global Calderón-Zygmund type estimates for the Hessian of viscosity solutions under small-aperture conditions.
Demonstrated applications to Sobolev estimates with variable exponents and the analysis of obstacle problems featuring oblique boundary conditions.

Cite This Study

Junior da S. Bessa (2026) studied this question.

synapsesocial.com/papers/6aa7b29f0926e14a848b105b https://doi.org/10.1142/s0219530526500776

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Implication

Theoretical analysis demonstrates global Calderón-Zygmund estimates in fully nonlinear elliptic equations with oblique boundaries, indicating broad applicability to obstacle problems.

Global Lorentz-type regularity for non-convex fully nonlinear elliptic equations with oblique boundary conditions and applications

Discussion

Member takes

Implication

Key Points

Cite This Study

Global Lorentz-type regularity for non-convex fully nonlinear elliptic equations with oblique boundary conditions and applications

Discussion

Member takes

Implication

Key Points

Cite This Study

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