ON THE TRACE OPERATOR FOR FUNCTIONS OF BOUNDED A-VARIATION

Breit D, Diening L, Gmeineder F (2020)
ANALYSIS & PDE 13(2): 559-594.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Breit, Dominic; Diening, LarsUniBi ; Gmeineder, Franz
Abstract / Bemerkung
We consider the space BVA(Omega) of functions of bounded A-variation. For a given first-order linear homogeneous differential operator with constant coefficients A, this is the space of L-1-functions u : Omega -> R-N such that the distributional differential expression Au is a finite (vectorial) Radon measure. We show that for Lipschitz domains Omega subset of R-n, BVA(Omega)-functions have an L-1(partial derivative Omega)-trace if and only if A is C-elliptic (or, equivalently, if the kernel of A is finite-dimensional). The existence of an L-1(partial derivative Omega)-trace was previously only known for the special cases that Au coincides either with the full or the symmetric gradient of the function u (and hence covered the special cases BV or BD). As a main novelty, we do not use the fundamental theorem of calculus to construct the trace operator (an approach which is only available in the BV- and BD-settings) but rather compare projections onto the nullspace of A as we approach the boundary. As a sample application, we study the Dirichlet problem for quasiconvex variational functionals with linear growth depending on Au.
Stichworte
trace operator; functions of bounded A-variation; linear growth; functionals
Erscheinungsjahr
2020
Zeitschriftentitel
ANALYSIS & PDE
Band
13
Ausgabe
2
Seite(n)
559-594
ISSN
1948-206X
Page URI
https://pub.uni-bielefeld.de/record/2942742

Zitieren

Breit D, Diening L, Gmeineder F. ON THE TRACE OPERATOR FOR FUNCTIONS OF BOUNDED A-VARIATION. ANALYSIS & PDE. 2020;13(2):559-594.
Breit, D., Diening, L., & Gmeineder, F. (2020). ON THE TRACE OPERATOR FOR FUNCTIONS OF BOUNDED A-VARIATION. ANALYSIS & PDE, 13(2), 559-594. doi:10.2140/apde.2020.13.559
Breit, D., Diening, L., and Gmeineder, F. (2020). ON THE TRACE OPERATOR FOR FUNCTIONS OF BOUNDED A-VARIATION. ANALYSIS & PDE 13, 559-594.
Breit, D., Diening, L., & Gmeineder, F., 2020. ON THE TRACE OPERATOR FOR FUNCTIONS OF BOUNDED A-VARIATION. ANALYSIS & PDE, 13(2), p 559-594.
D. Breit, L. Diening, and F. Gmeineder, “ON THE TRACE OPERATOR FOR FUNCTIONS OF BOUNDED A-VARIATION”, ANALYSIS & PDE, vol. 13, 2020, pp. 559-594.
Breit, D., Diening, L., Gmeineder, F.: ON THE TRACE OPERATOR FOR FUNCTIONS OF BOUNDED A-VARIATION. ANALYSIS & PDE. 13, 559-594 (2020).
Breit, Dominic, Diening, Lars, and Gmeineder, Franz. “ON THE TRACE OPERATOR FOR FUNCTIONS OF BOUNDED A-VARIATION”. ANALYSIS & PDE 13.2 (2020): 559-594.

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