Sökning: "Sobolev space"

Hittade 5 uppsatser innehållade orden Sobolev space.

1. 1. Multiple Phase Hele-Shaw Flows

   Master-uppsats, KTH/Matematik (Avd.)

   Författare :Karl Jonsson; [2014]
   Nyckelord :;

   Sammanfattning : A one phase Hele-Shaw flow, described by a domain D(t) (t represents time) in the plane is the flow of a liquid injected at a constant rate in the separation between two narrowly separated parallel planes. This thesis deals with the formulation and proof of existence for a multiple phase Hele-Shaw flow in arbitrary dimension R^n exhibiting separation of the phases. LÄS MER

3. 2. Radiella vikter i Rn och lokala dimensioner

   Master-uppsats, Linköpings universitet/Matematik och tillämpad matematik; Linköpings universitet/Tekniska högskolan

   Författare :Hanna Svensson; [2014]
   Nyckelord :Admissible weight; annulus; ball; capacity; doubling measure; exponent sets; measure; Poincaré inequality; Sobolev space; weight.; Admissibel vikt; dubblerande mått; exponentmängder; kapacitet; klot; mått; Poincarés olikhet; ringar; sobolevrum; vikt.;

   Sammanfattning : Kapaciteter kan vara till stor nytta, bland annat då partiella differentialekvationer ska lösas. Kapaciteter är dock i många fall väldigt svåra att beräkna exakt, speciellt i viktade rum. LÄS MER

4. 3. Lebesgue points, Hölder continuity and Sobolev functions

   Magister-uppsats, Matematiska institutionen

   Författare :John Karlsson; [2009]
   Nyckelord :Lebesgue point; Hausdorff dimension; Hausdorff measure; Hölder continuity; Maximal function; Poincaré inequality; Sobolev space; Uniform continuity;

   Sammanfattning : This paper deals with Lebesgue points and studies properties of the set of Lebesgue points for various classes of functions. We consider continuous functions, L1 functions and Sobolev functions. In the case of uniformly continuous functions and Hölder continuous functions we develop a characterization in terms of Lebesgue points. LÄS MER

5. 4. A counterexample concerning nontangential convergence for the solution to the time-dependent Schrödinger equation

   Magister-uppsats, Matematiska och systemtekniska institutionen

   Författare :Karoline Johansson; [2007]
   Nyckelord :Time-dependent Schrödinger equation; counterexample; nontangential convergence;

   Sammanfattning : Abstract: Considering the Schrödinger equation $\Delta_x u = i\partial{u}/\partial{t}$, we have a solution $u$ on the form $$u(x, t)= (2\pi)^{-n} \int_{\RR} {e^{i x\cdot \xi}e^{it|\xi|^2}\widehat{f}(\xi)}\, d \xi, x \in \RR, t \in \mathbf{R}$$ where $f$ belongs to the Sobolev space. It was shown by Sjögren and Sjölin, that assuming $\gamma : \mathbf{R}_+ \rightarrow \mathbf{R}_+ $ being a strictly increasing function, with $\gamma(0) = 0$ and $u$ and $f$ as above, there exists an $f \in H^{n/2} (\RR)$ such that $u$ is continuous in $\{ (x, t); t>0 \}$ and $$\limsup_{(y,t)\rightarrow (x,0),|y-x|<\gamma (t), t>0} |u(y,t)|= + \infty$$ for all $x \in \RR$. LÄS MER

7. 5. Upper gradients and Sobolev spaces on metric spaces

   Uppsats för yrkesexamina på grundnivå, Matematiska institutionen

   Författare :David Färm; [2006]
   Nyckelord :capacity; measure; metric space; Sobolev space; upper gradient;

   Sammanfattning : The Laplace equation and the related p-Laplace equation are closely associated with Sobolev spaces. During the last 15 years people have been exploring the possibility of solving partial differential equations in general metric spaces by generalizing the concept of Sobolev spaces. LÄS MER