2008, 1(3): 481-504. doi: 10.3934/dcdss.2008.1.481

Partial differential equations with non-Euclidean geometries

1. 

Mathematisches Institut, Universität Bonn, Beringstrasse 1, D - 53115 Bonn, Germany

Received  February 2008 Revised  March 2008 Published  June 2008

Coifman and Weiss initiated the study of singular integral operators on spaces of homogeneous type. We study partial differential equations with a non-Euclidean geometry and we obtain weighted estimates using the theory of Muckenhoupt weights on related spaces of homogeneous type. Examples include squares of vector fields, elliptic operators with a drift and the Oseen operator.
Citation: Herbert Koch. Partial differential equations with non-Euclidean geometries. Discrete & Continuous Dynamical Systems - S, 2008, 1 (3) : 481-504. doi: 10.3934/dcdss.2008.1.481
[1]

Mads Kyed. On a mapping property of the Oseen operator with rotation. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1315-1322. doi: 10.3934/dcdss.2013.6.1315

[2]

Jiří Neustupa. On $L^2$-Boundedness of a $C_0$-Semigroup generated by the perturbed oseen-type operator arising from flow around a rotating body. Conference Publications, 2007, 2007 (Special) : 758-767. doi: 10.3934/proc.2007.2007.758

[3]

Steve Hofmann, Dorina Mitrea, Marius Mitrea, Andrew J. Morris. Square function estimates in spaces of homogeneous type and on uniformly rectifiable Euclidean sets. Electronic Research Announcements, 2014, 21: 8-18. doi: 10.3934/era.2014.21.8

[4]

Tony Liimatainen, Mikko Salo. Nowhere conformally homogeneous manifolds and limiting Carleman weights. Inverse Problems & Imaging, 2012, 6 (3) : 523-530. doi: 10.3934/ipi.2012.6.523

[5]

Pascal Auscher, Sylvie Monniaux, Pierre Portal. The maximal regularity operator on tent spaces. Communications on Pure & Applied Analysis, 2012, 11 (6) : 2213-2219. doi: 10.3934/cpaa.2012.11.2213

[6]

Daniel Grieser. A natural differential operator on conic spaces. Conference Publications, 2011, 2011 (Special) : 568-577. doi: 10.3934/proc.2011.2011.568

[7]

Daniel Guan. Classification of compact complex homogeneous spaces with invariant volumes. Electronic Research Announcements, 1997, 3: 90-92.

[8]

Daniel Guan. Classification of compact homogeneous spaces with invariant symplectic structures. Electronic Research Announcements, 1997, 3: 52-54.

[9]

Maxim Sølund Kirsebom. Extreme value theory for random walks on homogeneous spaces. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4689-4717. doi: 10.3934/dcds.2014.34.4689

[10]

Laurent Denis, Anis Matoussi, Jing Zhang. The obstacle problem for quasilinear stochastic PDEs with non-homogeneous operator. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5185-5202. doi: 10.3934/dcds.2015.35.5185

[11]

Rafael De La Llave, R. Obaya. Regularity of the composition operator in spaces of Hölder functions. Discrete & Continuous Dynamical Systems - A, 1999, 5 (1) : 157-184. doi: 10.3934/dcds.1999.5.157

[12]

Guoqing Zhang, Jia-yu Shao, Sanyang Liu. Linking solutions for N-laplace elliptic equations with Hardy-Sobolev operator and indefinite weights. Communications on Pure & Applied Analysis, 2011, 10 (2) : 571-581. doi: 10.3934/cpaa.2011.10.571

[13]

Laurent Amour, Jérémy Faupin. Inverse spectral results in Sobolev spaces for the AKNS operator with partial informations on the potentials. Inverse Problems & Imaging, 2013, 7 (4) : 1115-1122. doi: 10.3934/ipi.2013.7.1115

[14]

Harald Fripertinger. The number of invariant subspaces under a linear operator on finite vector spaces. Advances in Mathematics of Communications, 2011, 5 (2) : 407-416. doi: 10.3934/amc.2011.5.407

[15]

Simona Fornaro, Abdelaziz Rhandi. On the Ornstein Uhlenbeck operator perturbed by singular potentials in $L^p$--spaces. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5049-5058. doi: 10.3934/dcds.2013.33.5049

[16]

Nakao Hayashi, Pavel I. Naumkin. Modified wave operator for Schrodinger type equations with subcritical dissipative nonlinearities. Inverse Problems & Imaging, 2007, 1 (2) : 391-398. doi: 10.3934/ipi.2007.1.391

[17]

Changguang Dong. Separated nets arising from certain higher rank $\mathbb{R}^k$ actions on homogeneous spaces. Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4231-4238. doi: 10.3934/dcds.2017180

[18]

Earl Berkson. Fourier analysis methods in operator ergodic theory on super-reflexive Banach spaces. Electronic Research Announcements, 2010, 17: 90-103. doi: 10.3934/era.2010.17.90

[19]

Angelo Favini, Yakov Yakubov. Regular boundary value problems for ordinary differential-operator equations of higher order in UMD Banach spaces. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 595-614. doi: 10.3934/dcdss.2011.4.595

[20]

Matthias Gerdts, Stefan Horn, Sven-Joachim Kimmerle. Line search globalization of a semismooth Newton method for operator equations in Hilbert spaces with applications in optimal control. Journal of Industrial & Management Optimization, 2017, 13 (1) : 47-62. doi: 10.3934/jimo.2016003

2016 Impact Factor: 0.781

Metrics

  • PDF downloads (3)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]