Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, , 164 - 175, 15.09.2023
https://doi.org/10.33205/cma.1324774

Öz

Kaynakça

  • A. Belläche: The Tangent Space in Sub-Riemannian Geometry, in: Sub-Riemannian Geometry; A. Belläche, J. J. Risler, Eds.; Progress in Mathematics; Birkhäuser: Basel, Switzerland, 144 (1996), 1–78.
  • R. Beals, B. Gaveau, P. Greiner: On a Geometric Formula for the Fundamental Solution of Subelliptic Laplacians, Math. Nachr., 181 (1996), 81–163.
  • T. Bieske, K. Blackwell: Generalizations of the Drift p-Laplace Equation in the Heisenberg Group and a Class of Grushin-type Planes, (2019), submitted for publication, preprint available at https://arxiv.org/abs/1906.01467.
  • T. Bieske, K. Childers: Generalizations of a Laplacian-type Equation in the Heisenberg Group and a Class of Grushin-type Spaces, Proc. Amer. Math. Soc., 142 (3) (2013), 989–1003.
  • T. Bieske, J. Gong: The p-Laplacian Equation on a Class of Grushin-Type Spaces, Amer. Math. Society, 134 (2006), 3585–3594.
  • T. Bieske, Z. Forrest: Existence and uniqueness of viscosity solutions to the infinity Laplacian relative to a class of Grushin-type vector fields, Constr. Math. Anal., 6 (2) (2023), 77–89.

Generalizations of the drift Laplace equation over the quaternions in a class of Grushin-type spaces

Yıl 2023, , 164 - 175, 15.09.2023
https://doi.org/10.33205/cma.1324774

Öz

Beals, Gaveau, and Greiner established a formula for the fundamental solution to the Laplace equation with drift term in Grushin-type planes. The first author and Childers expanded these results by invoking a p-Laplace type generalization that encompasses these formulas while the authors explored a different natural generalization of the p-Laplace equation with drift term that also encompasses these formulas. In both, the drift term lies in the complex domain. We extend these results by considering a drift term in the quaternion realm and show our solutions are stable under limits as p tends to infinity.

Kaynakça

  • A. Belläche: The Tangent Space in Sub-Riemannian Geometry, in: Sub-Riemannian Geometry; A. Belläche, J. J. Risler, Eds.; Progress in Mathematics; Birkhäuser: Basel, Switzerland, 144 (1996), 1–78.
  • R. Beals, B. Gaveau, P. Greiner: On a Geometric Formula for the Fundamental Solution of Subelliptic Laplacians, Math. Nachr., 181 (1996), 81–163.
  • T. Bieske, K. Blackwell: Generalizations of the Drift p-Laplace Equation in the Heisenberg Group and a Class of Grushin-type Planes, (2019), submitted for publication, preprint available at https://arxiv.org/abs/1906.01467.
  • T. Bieske, K. Childers: Generalizations of a Laplacian-type Equation in the Heisenberg Group and a Class of Grushin-type Spaces, Proc. Amer. Math. Soc., 142 (3) (2013), 989–1003.
  • T. Bieske, J. Gong: The p-Laplacian Equation on a Class of Grushin-Type Spaces, Amer. Math. Society, 134 (2006), 3585–3594.
  • T. Bieske, Z. Forrest: Existence and uniqueness of viscosity solutions to the infinity Laplacian relative to a class of Grushin-type vector fields, Constr. Math. Anal., 6 (2) (2023), 77–89.
Toplam 6 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Lie Grupları, Harmonik ve Fourier Analizi, Temel Matematik (Diğer)
Bölüm Makaleler
Yazarlar

Thomas Bieske 0000-0003-2029-0562

Keller Blackwell Bu kişi benim 0000-0003-3588-9199

Erken Görünüm Tarihi 25 Ağustos 2023
Yayımlanma Tarihi 15 Eylül 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

APA Bieske, T., & Blackwell, K. (2023). Generalizations of the drift Laplace equation over the quaternions in a class of Grushin-type spaces. Constructive Mathematical Analysis, 6(3), 164-175. https://doi.org/10.33205/cma.1324774
AMA Bieske T, Blackwell K. Generalizations of the drift Laplace equation over the quaternions in a class of Grushin-type spaces. CMA. Eylül 2023;6(3):164-175. doi:10.33205/cma.1324774
Chicago Bieske, Thomas, ve Keller Blackwell. “Generalizations of the Drift Laplace Equation over the Quaternions in a Class of Grushin-Type Spaces”. Constructive Mathematical Analysis 6, sy. 3 (Eylül 2023): 164-75. https://doi.org/10.33205/cma.1324774.
EndNote Bieske T, Blackwell K (01 Eylül 2023) Generalizations of the drift Laplace equation over the quaternions in a class of Grushin-type spaces. Constructive Mathematical Analysis 6 3 164–175.
IEEE T. Bieske ve K. Blackwell, “Generalizations of the drift Laplace equation over the quaternions in a class of Grushin-type spaces”, CMA, c. 6, sy. 3, ss. 164–175, 2023, doi: 10.33205/cma.1324774.
ISNAD Bieske, Thomas - Blackwell, Keller. “Generalizations of the Drift Laplace Equation over the Quaternions in a Class of Grushin-Type Spaces”. Constructive Mathematical Analysis 6/3 (Eylül 2023), 164-175. https://doi.org/10.33205/cma.1324774.
JAMA Bieske T, Blackwell K. Generalizations of the drift Laplace equation over the quaternions in a class of Grushin-type spaces. CMA. 2023;6:164–175.
MLA Bieske, Thomas ve Keller Blackwell. “Generalizations of the Drift Laplace Equation over the Quaternions in a Class of Grushin-Type Spaces”. Constructive Mathematical Analysis, c. 6, sy. 3, 2023, ss. 164-75, doi:10.33205/cma.1324774.
Vancouver Bieske T, Blackwell K. Generalizations of the drift Laplace equation over the quaternions in a class of Grushin-type spaces. CMA. 2023;6(3):164-75.