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Ανισότητες Sobolev και εφαρμογέςΤαβουλάρης, Νικόλαος Κ. 24 June 2007 (has links)
Η παρούσα διατριβή εντάσσεται ερευνητικά στην περιοχή της μη γραμμικής ανάλυσης και ειδικότερα στην εύρεση βέλτιστων σταθερών για ανισότητες Sobolev στο χώρο Rn με ανώτερης τάξης δεκαδικές παραγώγους. Επίσης, δίνονται οι αντίστοιχες βέλτιστες σταθερές αυτών των ανισοτήτων πάνω στη σφαίρα Sn με τη χρησιμοποίηση ως βασικού εργαλείου την στερεογραφική προβολή. Τέλος, σαν μια εφαρμογή των ευρεθέντων ανισοτήτων έχουμε ένα θεώρημα σχετικό με αυτό των Rellich-Kondrashov και το οποίο είναι εξαιρετικής σημασίας, ιδιαίτερα στο λογισμό των μεταβολών.
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Sobolev spacesClemens, Jason January 1900 (has links)
Master of Science / Department of Mathematics / Marianne Korten / The goal for this paper is to present material from Gilbarg and Trudinger’s Elliptic
Partial Differential Equations of Second Order chapter 7 on Sobolev spaces, in a manner easily accessible to a beginning graduate student. The properties of weak derivatives and there relationship to conventional concepts from calculus are the main focus, that is when do weak and strong derivatives coincide. To enable the progression into the primary focus, the process of mollification is presented and is widely used in estimations. Imbedding theorems and compactness results are briefly covered in the final sections. Finally, we add some exercises at the end to illustrate the use of the ideas presented throughout the paper.
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Discontinuous Galerkin methods on shape-regular and anisotropic meshesGeorgoulis, Emmanuil H. January 2003 (has links)
No description available.
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The Best constant for a general Sobolev-Hardy inequality.January 1991 (has links)
by Chu Chiu Wing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Bibliography: leaves 31-32. / Introduction / Chapter Section 1. --- A Minimization Problem / Chapter Section 2. --- Radial Symmetry of The Solution / Chapter Section 3. --- Proof of The Main Theorem / References
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Sobolevova věta o vnoření na oblastech s nelipschitzovskou hranicí / Sobolev embedding theorem on domains without Lipschitz boundaryRoskovec, Tomáš January 2012 (has links)
We study the Sobolev embeddings theorem and formulate modified theorems on domains with nonlipschitz boundary. The Sobolev embeddings the- orem on a domain with Lipschitz boundary claims f ∈ W1,p ⇒ f ∈ Lp∗ (p) , kde p∗ (p) = np n − p . The function p∗ (p) is continuous and even smooth. We construct a domain with nonlipschitz boundary and function of the optimal embedding i.e. analogy of p∗ (p) is not continous. In the first part, according to [1], we construct the domain with the point of discontinuity for p = n = 2. Though we used known construction of domain, we prove this by using more simple and elegant methods. In the second part of thesis we suggest the way how to generalize this model domain and shift the point of discontinuity to other point than p = n = 2.
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Οικογένειες συναρτησιακών ανισοτήτων / Famillies of functional inequalitiesΖάχος, Αναστάσιος 17 May 2007 (has links)
Αρχικά εισάγονται οι ανισότητες Sobolev για τις οποίες ο ρόλος της διάστασης είναι θεμελιώδης και στην συνέχεια δείχνουμε τον τρόπο με τιν οποίο αυτές εξασθενίζουν. Ακόμα θα δούμε πως με τη βοήθεια των ανισοτήτων εντροπίας ενέργειας γίνεται κατανοητός ο απειροδιάστατος χαρακτήρας της λογαριθμικής ανισότητας Sobolev. / Firstly we introduce the Sobolev inequalities that the role of the dimension is vital. Furthermore, we will show the way that they have been weakened. We see also with the help of the inequalities of Entropy-Energy how we can clarify the infinite dimensional character of the logarithmic Sobolev inequalities.
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A constructive method for finding critical point of the Ginzburg-Landau energy functionalKazemi, Parimah. Neuberger, J.W. January 2008 (has links)
Thesis (Ph. D.)--University of North Texas, August, 2008. / Title from title page display. Includes bibliographical references.
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Nicht-diagonale Interpolation von klassischen FunktionenräumenBöcking, Joachim. January 1900 (has links)
Thesis (doctoral)--Universität Bonn, 1993. / Includes bibliographical references (p. 117-118).
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Strichartz estimates for wave equations with coefficients of Sobolev regularity /Blair, Matthew D. January 2005 (has links)
Thesis (Ph. D.)--University of Washington, 2005. / Vita. Includes bibliographical references (leaves 87-88).
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Limitação uniforme de minimizantes de funcionais não suavesFormehl, Thiago January 2016 (has links)
Orientador : Prof. Dr. Jurandir Ceccon / Dissertação (mestrado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Matemática. Defesa: Curitiba, 24/02/2016 / Inclui referências : f. 63-64 / Área de concentração: Matematica / Resumo: Neste trabalho, analisamos a regularidade L1 de minimizantes para o funcional _ : W1;2 0 (;Rk) ! R dado por _(u) = Z jruj2dx ?? Z G(u)dx; restrito ao conjunto EF = fu 2 W1;2 0 (;Rk) : R F(u)dx = 1g, em que é um subconjunto aberto e limitado de Rn, F e G são funções contínuas e homogêneas de graus 2_ e 2, respectivamente. Previamente algumas condições são estabelecidas para a existência desses minimizantes. Além disso, supondo F e G funções de classe C1 e definindo f(u) = 1 2_ rF(u) e g(u) = 1 2 rG(u), alguns resultados sobre a existência de soluções não triviais para o sistema 8< : ??_u = f(u) + g(u) em ; u = 0 sobre @ são demonstrados. Palavras-chave: Minimização não suave; regularidade; potenciais elípticos; expoente crítico de Sobolev. / Abstract: In this work, we analyse the L1 regularity of minimizers for the functional _ : W1;2 0 (;Rk) ! R given by _(u) = Z jruj2dx ?? Z G(u)dx; constrained to the set EF = fu 2 W1;2 0 (;Rk) : R F(u)dx = 1g, where is bounded open subset of Rn, F and G are homogeneous continuous functions of degree 2_ and 2, respectively. Previously some conditions are established for existence of these minimizers. Moreover, assuming F and G are C1 functions and setting f(u) = 1 2_ rF(u) and g(u) = 1 2 rG(u), some results about existence of nontrivial solutions to the system 8< : ??_u = f(u) + g(u) em ; u = 0 sobre @ are demonstrated. Keywords: Non-smooth minimization; regularity; potential elliptic; critical Sobolev exponents.
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