Geodesic
Elements of Potential Theory on Carnot Groups
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 2, pp. 94-98

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We propose and study elements of potential theory for the sub-Laplacian on homogeneous Carnot groups. In particular, we show the continuity of the single-layer potential and establish Plemelj-type jump relations for the double-layer potential. As a consequence, we derive a formula for the trace on smooth surfaces of the Newton potential for the sub-Laplacian. Using this, we construct a sub-Laplacian version of Kac's boundary value problem.
Keywords: sub-Laplacian, integral boundary condition, homogeneous Carnot group, Newton potential, layer potentials. 
@article{FAA_2018_52_2_a10,
     author = {M. V. Ruzhansky and D. Suragan},
     title = {Elements of {Potential} {Theory} on {Carnot} {Groups}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {94--98},
     publisher = {mathdoc},
     volume = {52},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2018_52_2_a10/}
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M. V. Ruzhansky; D. Suragan. Elements of Potential Theory on Carnot Groups. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 2, pp. 94-98. http://geodesic.mathdoc.fr/item/FAA_2018_52_2_a10/