Existence and regularity for a $p$-Laplacian problem in $\mathbb{R}^N$ with singular, convective, critical reaction

Laura Baldelli; Umberto Guarnotta

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arXiv · 2401.15959

Existence and regularity for a $p$-Laplacian problem in $\mathbb{R}^N$ with singular, convective, critical reaction

Laura Baldelli·Umberto Guarnotta

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Abstract

We prove an existence result for a $p$-Laplacian problem set in the whole Euclidean space and exhibiting a critical term perturbed by a singular, convective reaction. The approach used combines variational methods, truncation techniques, and concentration compactness arguments, together with set-valued analysis and fixed point theory. De Giorgi's technique, a priori gradient estimates, and nonlinear regularity theory are employed to get local $C^{1,\alpha}$ regularity of solutions, as well as their pointwise decay at infinity. The result is new even in the non-singular case, also for the Laplacian.

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Laura Baldelli, Umberto Guarnotta. 2024-01-29. Existence and regularity for a $p$-Laplacian problem in $\mathbb{R}^N$ with singular, convective, critical reaction. https://arxiv.org/abs/2401.15959

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