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• 1. Acker, Andrew
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Convex configurations for solutions to semilinear elliptic problems in convex rings2006Inngår i: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 31, nr 9, s. 1273-1287Artikkel i tidsskrift (Fagfellevurdert)

For a given convex ring Omega = Omega(2)\(Omega) over bar (1) and an L-1 function f : Omega x R -> R+ we show, under suitable assumptions on f, that there exists a solution (in the weak sense) to Delta(p)u = f(x, u) in Omega u = 0 on partial derivative Omega(2) u = M on partial derivative Omega(1) with {x is an element of Omega : u(x) > s} boolean OR Omega(1) convex, for all s is an element of (0, M).

• 2. Ammann, Bernd
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Surgery and the Spinorial tau-Invariant2009Inngår i: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 34, nr 10, s. 1147-1179Artikkel i tidsskrift (Fagfellevurdert)

We associate to a compact spin manifold M a real-valued invariant (M) by taking the supremum over all conformal classes of the infimum inside each conformal class of the first positive Dirac eigenvalue, when the metrics are normalized to unit volume. This invariant is a spinorial analogue of Schoen's sigma-constant, also known as the smooth Yamabe invariant. We prove that if N is obtained from M by surgery of codimension at least 2 then (N) epsilon min{(M), n}, where n is a positive constant depending only on n=dim M. Various topological conclusions can be drawn, in particular that is a spin-bordism invariant below n. Also, below n the values of cannot accumulate from above when varied over all manifolds of dimension n.

• 3. Castella, F.
High frequency limit of the Helmholtz equation. II. Source on a general smooth manifold2002Inngår i: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 27, nr 04-mar, s. 607-651Artikkel i tidsskrift (Fagfellevurdert)
• 4.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
NTNU, Trondheim, Norway.
Regularity of a Parabolic Free Boundary Problem with Holder Continuous Coefficients2012Inngår i: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 37, nr 7, s. 1161-1185Artikkel i tidsskrift (Fagfellevurdert)

We consider the parabolic obstacle type problem Hu = f chi(Omega) in Q(1)(-), u = vertical bar del u vertical bar = 0 on Q(1)(-)\Omega, where Omega is an unknown open subset of Q(1)(-). This problem has its origin in parabolic potential theory. When f is merely Holder continuous, the usual method based on the use of a monotonicity formula does not apply. Nevertheless, we can, under a combination of energetic and geometric assumptions, prove the optimal C-x(1,1) boolean AND C-t(0,1) regularity of the solution.

• 5.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
Faculty of Mathematics and Physics, Stuttgart University.
Stability of the Magnetic Schrödinger Operator in a Waveguide2005Inngår i: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 30, nr 4-6, s. 539-565Artikkel i tidsskrift (Fagfellevurdert)

The spectrum of the Schrödinger operator in a quantum waveguide is known to be unstable in two and three dimensions. Any local enlargement of the waveguide produces eigenvalues beneath the continuous spectrum. Also, if the waveguide is bent, eigenvalues will arise below the continuous spectrum. In this paper a magnetic field is added into the system. The spectrum of the magnetic Schrödinger operator is proved to be stable under small local deformations and also under small bending of the waveguide. The proof includes a magnetic Hardy-type inequality in the waveguide, which is interesting in its own right.

• 6.
Department of Mathematics and Statistics, University of New Mexico.
KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
Automatic symmetrization and energy estimates using local operators for partial differential equations2007Inngår i: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 32, nr 7, s. 1129-1145Artikkel i tidsskrift (Fagfellevurdert)

We develop a method for automatically symmetrizing Petrowsky well-posed Cauchy problems for constant coefficient linear partial differential equations. The method is rooted in the Sturm sequence technique for establishing the location of the roots of a complex polynomial and can be automated using standard symbolic computation tools. In the special case of homogeneous strictly hyperbolic scalar equations, we show that the resulting estimates are strong enough to control all principal order derivatives and thus can be used in place of the Leray energies. We also illustrate the method by applying it to various problems of mixed type.

• 7.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
An inequality between Dirichlet and Neumann eigenvalues of the Heisenberg Laplacian2008Inngår i: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 33, nr 12, s. 2157-2163Artikkel i tidsskrift (Fagfellevurdert)

Let k and μk be the eigenvalues of the Dirichlet and Neumann problems, respectively, in a domain of finite measure in Rd, d1. Filonov has proved in a simple way that the inequality μk+1<k holds for the Laplacian. We extend his result to the Heisenberg Laplacian in three-dimensional domains which fulfill certain geometric conditions.

• 8.
Edinburgh University.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Application of Uniform Distribution to Homogenization of a Thin Obstacle Problem with p-Laplacian2014Inngår i: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 39, nr 10, s. 1870-1897Artikkel i tidsskrift (Fagfellevurdert)

In this paper we study the homogenization of p-Laplacian with thin obstacle in a perforated domain. The obstacle is defined on the intersection between a hyperplane and a periodic perforation. We construct the family of correctors for this problem and show that the solutions for the epsilon-problem converge to a solution of a minimization problem of similar form but with an extra term involving the mean capacity of the obstacle. The novelty of our approach is based on the employment of quasi-uniform convergence. As an application we obtain Poincare's inequality for perforated domains.

• 9. Karp, L.
KTH, Tidigare Institutioner                               , Matematik.
Regularity of a free boundary at the infinity point2000Inngår i: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 25, nr 12-Nov, s. 2055-2086Artikkel i tidsskrift (Fagfellevurdert)

Suppose there is a nonnegative function u and an open set Ohm subset of R-n(n greater than or equal to 3), satisfying Deltau = chi (Ohm) in B-r(e), u = \delu\ = 0 on B-r(e)\Ohm, where B-r(e) = {x : \x\ > r}. Under a certain thickness condition on R-n\Ohm, we prove that the boundary of {x:x/\x\(2) is an element of Ohm} is a graph of a C-1 function in a neighborhood of the origin. As a by-product of the method of the proof, we also obtain the following result: Replace chi (Ohm) by f chi (Ohm), with a certain assumptions on f. Then for any solution u which is asymptotically nonnegative at infinity, there holds lim(r-->infinity) (\Br\)/(\Ohm boolean AND Br\) is an element of {1/2,1}.

• 10.
Baylor University, United States .
The Hunter-Saxton System and the Geodesics on a Pseudosphere2013Inngår i: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 38, nr 5, s. 860-881Artikkel i tidsskrift (Fagfellevurdert)

We show that the two-component Hunter-Saxton system with negative coupling constant describes the geodesic flow on an infinite-dimensional pseudosphere. This approach yields explicit solution formulae for the Hunter-Saxton system. Using this geometric intuition, we conclude by constructing global weak solutions. The main novelty compared with similar previous studies is that the metric is indefinite.

• 11. Szepessy, Anders
An existence result for scalar conservation laws using measure valued solutions1989Inngår i: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 14, nr 10, s. 1329-1350Artikkel i tidsskrift (Fagfellevurdert)
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