Abstract. We find the fundamental solution to the P-Laplace equation in Grushin-type spaces. The ... more Abstract. We find the fundamental solution to the P-Laplace equation in Grushin-type spaces. The singularity occurs at the sub-Riemannian points, which naturally corresponds to finding the fundamental solution of a general-ized Grushin operator in Euclidean space. ...
This is a survey article about the regularity of solutions to the p-Laplace equation on Euclidean... more This is a survey article about the regularity of solutions to the p-Laplace equation on Euclidean spaces. Such functions can be characterized as minimizers to certain non-linear energy functionals. The methods presented here, originally due to DeGiorgi, show that Harnack's inequality and Hölder continuity follow solely from this minimization property.
We show that quasi-minimizers of non-homogeneous energy functionals are locally Hölder continuous... more We show that quasi-minimizers of non-homogeneous energy functionals are locally Hölder continuous and satisfy the Harnack inequality on metric measure spaces. We assume that the space is doubling and supports a Poincaré inequality. The proof is based on the De Giorgi method, combined with the expansion of positivity technique.
In this paper we prove a new version of the Schoenflies extension theorem for collared domains Ω ... more In this paper we prove a new version of the Schoenflies extension theorem for collared domains Ω and Ω ′ in R n : for p ∈ [1, n), locally bi-Lipschitz homeomorphisms from Ω to Ω ′ with locally p-integrable, second-order weak derivatives admit homeomorphic extensions of the same regularity.
In this paper we investigate the linear algebraic properties of Weaver's theory of (metric) deriv... more In this paper we investigate the linear algebraic properties of Weaver's theory of (metric) derivations. For k = 1, 2, we show that measures on R k that induce rank-k modules of derivations must be absolutely continuous to Lebesgue k-measure.
Abstract. We find the fundamental solution to the P-Laplace equation in Grushin-type spaces. The ... more Abstract. We find the fundamental solution to the P-Laplace equation in Grushin-type spaces. The singularity occurs at the sub-Riemannian points, which naturally corresponds to finding the fundamental solution of a general-ized Grushin operator in Euclidean space. ...
This is a survey article about the regularity of solutions to the p-Laplace equation on Euclidean... more This is a survey article about the regularity of solutions to the p-Laplace equation on Euclidean spaces. Such functions can be characterized as minimizers to certain non-linear energy functionals. The methods presented here, originally due to DeGiorgi, show that Harnack's inequality and Hölder continuity follow solely from this minimization property.
We show that quasi-minimizers of non-homogeneous energy functionals are locally Hölder continuous... more We show that quasi-minimizers of non-homogeneous energy functionals are locally Hölder continuous and satisfy the Harnack inequality on metric measure spaces. We assume that the space is doubling and supports a Poincaré inequality. The proof is based on the De Giorgi method, combined with the expansion of positivity technique.
In this paper we prove a new version of the Schoenflies extension theorem for collared domains Ω ... more In this paper we prove a new version of the Schoenflies extension theorem for collared domains Ω and Ω ′ in R n : for p ∈ [1, n), locally bi-Lipschitz homeomorphisms from Ω to Ω ′ with locally p-integrable, second-order weak derivatives admit homeomorphic extensions of the same regularity.
In this paper we investigate the linear algebraic properties of Weaver's theory of (metric) deriv... more In this paper we investigate the linear algebraic properties of Weaver's theory of (metric) derivations. For k = 1, 2, we show that measures on R k that induce rank-k modules of derivations must be absolutely continuous to Lebesgue k-measure.
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Papers by Jasun Gong