We consider the equation - Δ p u = f (u) {-Deltap}u=f(u)} in a smooth bounded domain of R n {mathbb{R}-{n}}, where Δ p {Deltap}} is the p-Laplace operator. Explicit examples of unbounded stable energy solutions are known if n ≥ p + 4 p p - 1 {ngeq p+frac{4p}{p-1}}. Instead, when n < p + 4 p p - 1 {n
Optimal regularity of stable solutions to nonlinear equations involving the p-Laplacian / X. Cabré, P. Miraglio, M. Sanchón. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8258. - 15:4(2022), pp. 749-785. [10.1515/acv-2020-0055]
Optimal regularity of stable solutions to nonlinear equations involving the p-Laplacian
P. MiraglioPenultimo
;
2022
Abstract
We consider the equation - Δ p u = f (u) {-Deltap}u=f(u)} in a smooth bounded domain of R n {mathbb{R}-{n}}, where Δ p {Deltap}} is the p-Laplace operator. Explicit examples of unbounded stable energy solutions are known if n ≥ p + 4 p p - 1 {ngeq p+frac{4p}{p-1}}. Instead, when n < p + 4 p p - 1 {n
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