An Introduction to Sobolev Spaces

Pişkin, Erhan
Okutmuştur, Baver
Sobolev spaces were firstly defined by the Russian mathematician, Sergei L. Sobolev (1908-1989) in the 1930s. Several properties of these spaces have been studied by mathematicians until today. Functions that account for existence and uniqueness, asymptotic behavior, blow up, stability and instability of the solution of many differential equations that occur in applied and in engineering sciences are carried out with the help of Sobolev spaces and embedding theorems in these spaces. An Introduction to Sobolev Spaces provides a brief introduction to Sobolev spaces at a simple level with illustrated examples. Readers will learn about the properties of these types of vector spaces and gain an understanding of advanced differential calculus and partial difference equations that are related to this topic. The contents of the book are suitable for undergraduate and graduate students, mathematicians, and engineers who have an interest in getting a quick, but carefully presented, mathematically sound, basic knowledge about Sobolev Spaces.


On the isomorphic classification of the cartesian products of köthe spaces
Taştüner, Emre; Yurdakul, Murat Hayrettin; Department of Mathematics (2019)
In 1973, V. P. Zahariuta formed a method to classify the Cartesian products of locally convex spaces by using the theory of Fredholm operators. In this thesis, we gave modifications done in the method of Zahariuta. Then by using them, we studied the isomorphic classifications of Cartesian products of l^p and l^q type Köthe sequence spaces.
Investigation of novel topological indices and their applications in organic chemistry
Gümüş, Selçuk; Türker, Burhan Lemi; Department of Chemistry (2009)
Numerical descriptors, beginning with Wiener, and then named topological indices by Hosoya, have gained gradually increasing importance along with other descriptors for use in QSAR and QSPR studies. Being able to estimate the physical or chemical properties of a yet nonexistent substance as close as possible is very important due to huge consumption of time and money upon direct synthesis. In addition, one may face safety problem as in the case of explosives. There have been almost hundred topological indic...
Some New Completeness Properties in Topological Spaces
Vural, Çetin; Önal, Süleyman (null; 2017-06-30)
One of the most widely known completeness property is the completeness of metric spaces and the other one being of a topological space in the sense of Cech. It is well known that a metrizable space X is completely metrizable if and only if X is Cech-complete. One of the generalisations of completeness of metric spaces is subcompactness. It has been established that, for metrizable spaces, subcompactness is equivalent to Cech-completeness. Also the concept of domain representability can be considered as a co...
An investigation of Turkish static spatial semantics in terms of lexical variety: an eye tracking study
Ertekin, Şeyma Nur; Acartürk, Cengiz; Department of Cognitive Sciences (2021-8)
The semantics of spatial terms has been attracting the attention of researchers for the past several decades. As an understudied language, Turkish presents an appropriate test bed for studying the generalizability of semantic characterization of spatial terms across languages. Turkish also exhibits unique characteristics, such as the use of locative case markers and being an agglutinative language. The present study reports an eye-tracking investigation of comprehension of spatial terms in Turkish by employ...
Strictly singular operators and isomorphisms of Cartesian products of power series spaces
Djakov, PB; Onal, S; Terzioglu, T; Yurdakul, Murat Hayrettin (1998-01-02)
V. P. Zahariuta, in 1973, used the theory of Fredholm operators to develop a method to classify Cartesian products of locally convex spaces. In this work we modify his method to study the isomorphic classification of Cartesian products of the kind E-0(p)(a) x E-infinity(q) (b) where 1 less than or equal to p, q < infinity, p not equal q, a = (a(n))(n=1)(infinity) and b = (b(n))(n=1)(infinity) are sequences of positive numbers and E-0(p)(a), E(infinity)q(b) are respectively l(p)-finite and l(q)-infinite type...
Citation Formats
E. Pişkin and B. Okutmuştur, An Introduction to Sobolev Spaces. 2021.