Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Supervisors info:
Γεράσιμος Μπαρμπάτης, Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Pier Domenico Lamberti, Αναπληρωτής Καθηγητής, Τμήμα Μαθηματικών, University of Padova (Πανεπιστήμιο της Πάντοβα)
Original Title:
Trace theorems for Sobolev spaces
Translated title:
Trace theorems for Sobolev spaces
Summary:
For Ω subset of R^N open set with boundary ∂Ω satisfying certain smoothness assumptions, we consider the Besov spaces on the boundary ∂Ω (with parameteres l,p) as the trace spaces of the Sobolev spaces on Ω (with parameteres l,p) . More specifically, first we consider the traces in R^(N−1) of functions defined on R^N and we prove that the trace operator T with domain of definition the Sobelev spaces in R^N (with parameters l,p) and range the L^p in R^(N−1) when applied in the Sobolev space in possitive of R^N and with the parameter p=1 it yields the Bessov spaces in R^(N-1) with parameters 1-1/p and p. Then we prove that the trace operator when applied to the Sobolev spaces of Ω and with parameters l,p it yields the Besov spaces on the boundary ∂Ω with parameters 1-1/p and p, where Ω subset of R^N an open set with C^l-boundary. For the case that the parameter p= 2, we approach the definition of the trace spaces with two other methods, namely using the Fourier transformation and using the spectral definition given by Auchmuty. Finally, we use the previous results to prove the existence of solution for the Dirichlet problem.
Main subject category:
Science
Keywords:
Trace Theorems, Sobolev spaces, Besov spaces, Dirichlet Problem
