By Diego Ricciotti
This works specializes in regularity concept for recommendations to the p-Laplace equation within the Heisenberg workforce. specifically, it provides particular proofs of smoothness for strategies to the non-degenerate equation and of Lipschitz regularity for strategies to the degenerate one. An introductory bankruptcy offers the elemental homes of the Heisenberg team, making the assurance self-contained. The atmosphere is the 1st Heisenberg staff, supporting to maintain the notation basic and make allowance the reader to target the middle of the idea and strategies within the box. extra, unique proofs make the paintings obtainable to scholars on the graduate level.
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Extra resources for p-Laplace Equation in the Heisenberg Group: Regularity of Solutions
At the end we present the Hilbert–Haar existence theory for the variational functional associated to the p-Laplace equation which allows to prove that solutions to the non degenerate equation are Lipschitz continuous in domains satisfying a strict convexity condition. 1 Definitions and Notations The p-Laplace equation, 1 < p < ∞ is divH δ 2 + |∇H u|2 p−2 2 ∇H u = 0 in Ω. 2) as will be explained in detail in Sect. 2. We will use the term non degenerate for the case δ > 0 and degenerate for δ = 0.
204(2), 439–470 (2004) 3. : BV spaces and rectifiability for Carnot-Carathéodory metrics: an introduction. NAFSA 7–Nonlinear Analysis. Function Spaces and Applications, vol. 7, pp. 72–132. Czech Academy of Sciences, Prague (2003) 4. : Embedding theorems into Lipschitz and BMO spaces and applications to quasilinear subelliptic differential equations. Publ. Mat. 40(2), 301–329 (1996) 5. : Lie Groups, Lie Algebras, and their Representations, vol. 102. Graduate Texts in Mathematics. Springer, New York (1984) (Reprint of the 1974 edition) Chapter 3 The p-Laplace Equation Abstract We give basic definitions and properties of the p-Laplace equation in the Heisenberg group.
River Edge (2003) 2. : Un teorema di esistenza e unicità per il problema dell’area minima in n variabili. Ann. Scuola Norm. Sup. Pisa 3(19), 233–249 (1965) 3. : On the weak continuity of elliptic operators and applications to potential theory. Am. J. Math. 124(2), 369–410 (2002) 4. : Regularity for variational problems in the Heisenberg group. 1) divH δ 2 + |∇H u|2 p−2 2 ∇H u = 0 in Ω for 1 < p < ∞. 44) with ∇H u L ∞ (D) ≤ M. 1) For this reason the results will be stated in terms of D instead of Ω, but since we are studying interior regularity and all the results are local, there is no loss of generality.
p-Laplace Equation in the Heisenberg Group: Regularity of Solutions by Diego Ricciotti