What question did this study set out to answer?

This research aims to establish the existence of solutions and energy bounds for a specific class of p-elliptic equations with lower-order terms.

April 3, 2026

Bojarski–Meyers Inequality for Solutions of a p-Elliptic Equation with Lower-Order Terms and the Zaremba Boundary Condition. The Critical Case

Key Points

This research aims to establish the existence of solutions and energy bounds for a specific class of p-elliptic equations with lower-order terms.
Proved the existence of solutions to the p-elliptic equation.
Demonstrated energy bounds for solutions.
Analyzed summability of the solution's gradient in a Lipschitz domain.
Established existence of a solution under the Zaremba boundary condition.
Showed improved gradient summability for solutions in bounded domains.
Confirmed energy bounds which constrain solution behavior.

Abstract

The existence of a solution and an energy bound are proven. The increased summability of the gradient of the solution to the Zaremba problem in a bounded strictly Lipschitz domain is also proved for a nonhomogeneous p -elliptic equation with low-order linear terms.

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Authors

A. G. Chechkina

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Institutions

Lomonosov Moscow State University

Ufa Institute of Chemistry

Institute of Mathematics with Computer Center

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A. G. Chechkina (Mon,) studied this question.

synapsesocial.com/papers/69cf5ede5a333a821460d85f — DOI: https://doi.org/10.1134/s0001434625605829

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Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Bojarski-Meyers estimate for a solution to the Zaremba problem for Poisson's equations with drift· 2025 · 2 citations
On the Zaremba Problem for Inhomogeneous p-Laplace Equation with Drift· 2025 · 1 citations
On the Zaremba problem for the $p$-elliptic equation· 2023 · 7 citations
Boyarsky–Meyers Estimate for Solutions to Zaremba Problem· 2022 · 24 citations
The Lp-integrability of the partial derivatives of A quasiconformal mapping· 1973 · 786 citations

Also consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Bojarski-Meyers estimate for a solution to the Zaremba problem for Poisson's equations with drift· 2025 · 2 citations
On the Zaremba Problem for Inhomogeneous p-Laplace Equation with Drift· 2025 · 1 citations
On the Zaremba problem for the $p$-elliptic equation· 2023 · 7 citations
Boyarsky–Meyers Estimate for Solutions to Zaremba Problem· 2022 · 24 citations
The Lp-integrability of the partial derivatives of A quasiconformal mapping· 1973 · 786 citations

Bojarski–Meyers Inequality for Solutions of a p-Elliptic Equation with Lower-Order Terms and the Zaremba Boundary Condition. The Critical Case

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Authors

Journals

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

Cite this study

Also consider

Also consider