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  • 1.
    Arnarson, Teitur
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Djehiche, Boualem
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Poghosyan, Michael
    Yerevan State Univ, Dept Math & Mech.
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    A PDE approach to regularity of solutions to finite horizon optimal switching problems2009In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 71, no 12, p. 6054-6067Article in journal (Refereed)
    Abstract [en]

    We study optimal 2-switching and n-switching problems and the corresponding system of variational inequalities. We obtain results on the existence of viscosity solutions for the 2-switching problem for various setups when the cost of switching is non-deterministic. For the n-switching problem we obtain regularity results for the solutions of the variational inequalities. The solutions are C-l,C-l-regular away for the free boundaries of the action sets.

  • 2.
    Ekholm, Tomas
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Kovarik, Hynek
    Laptev, Ari
    Hardy inequalities for p-Laplacians with Robin boundary conditions2015In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 128, p. 365-379Article in journal (Refereed)
    Abstract [en]

    In this paper we study the best constant in a Hardy inequality for the p-Laplace operator on convex domains with Robin boundary conditions. We show, in particular, that the best constant equals ((p-1)/p)(p) whenever Dirichlet boundary conditions are imposed on a subset of the boundary of non-zero measure. We also discuss some generalizations to non-convex domains.

  • 3.
    Jönsson, Ulf T.
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Megretski, Alexandre
    Analysis and computation of limit cycles for systems with separable nonlinearities2008In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 69, no 12, p. 4674-4693Article in journal (Refereed)
    Abstract [en]

    The variational system obtained by linearizing a dynamical system along a limit cycle is always non-invertible. This follows because the limit cycle is only a unique modulo time translation. It is shown that questions such as uniqueness, robustness, and computation of limit cycles can be addressed using a right inverse of the variational system. Small gain arguments are used in the analysis.

  • 4. Karakhanyan, A. L.
    et al.
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Boundary behaviour for a singular perturbation problem2016In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 138, p. 176-188Article in journal (Refereed)
    Abstract [en]

    In this paper we study the boundary behaviour of the family of solutions (uε) to singular perturbation problem δuε=βε(uε),(divides)uε(divides)≤1 in B1+=(xn>0)∩((divides)x(divides)<1), where a smooth boundary data f is prescribed on the flat portion of ∂B1+. Here βε((dot operator))=1εβ((dot operator)ε),β∈C0∞(0,1),β≥0,∫01β(t)=M>0 is an approximation of identity. If ∇f(z)=0 whenever f(z)=0 then the level sets ∂(uε>0) approach the fixed boundary in tangential fashion with uniform speed. The methods we employ here use delicate analysis of local solutions, along with elaborated version of the so-called monotonicity formulas and classification of global profiles.

  • 5. Kim, S.
    et al.
    Lee, K. -A
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    An elliptic free boundary arising from the jump of conductivity2017In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 161, p. 1-29Article in journal (Refereed)
    Abstract [en]

    In this paper we consider a quasilinear elliptic PDE, div(A(x,u)∇u)=0, where the underlying physical problem gives rise to a jump for the conductivity A(x,u), across a level surface for u. Our analysis concerns Lipschitz regularity for the solution u, and the regularity of the level surfaces, where A(x,u) has a jump and the solution u does not degenerate. In proving Lipschitz regularity of solutions, we introduce a new and unexpected type of ACF-monotonicity formula with two different operators, that might be of independent interest, and surely can be applied in other related situations. The proof of the monotonicity formula is done through careful computations, and (as a byproduct) a slight generalization to a specific type of variable matrix-valued conductivity is presented.

  • 6.
    Lenells, Jonatan
    Baylor University, United States .
    The Degasperis-Procesi equation on the half-line2013In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 76, no 1, p. 122-139Article in journal (Refereed)
    Abstract [en]

    We analyze a class of initial-boundary value problems for the Degasperis-Procesi equation on the half-line. Assuming that the solution u(x,t) exists, we show that it can be recovered from its initial and boundary values via the solution of a Riemann-Hilbert problem formulated in the plane of the complex spectral parameter k.

  • 7.
    Lindgren, Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Privat, Yannick
    A free boundary problem for the Laplacian with a constant Bernoulli-type boundary condition2007In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 67, no 8, p. 2497-2505Article in journal (Refereed)
    Abstract [en]

    We study a free boundary problem for the Laplace operator, where we impose a Bernoulli-type boundary condition. We show that there exists a solution to this problem. We use A. Beurling's technique, by defining two classes of sub- and super-solutions and a Perron argument. We try to generalize here a previous work of A. Henrot and H. Shahgholian. We extend these results in different directions.

  • 8.
    Sjödin, Tomas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    On the structure of partial balayage2007In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 67, no 1, p. 94-102Article in journal (Refereed)
    Abstract [en]

    We define partial balayage, construct it with classical potential-theoretic methods and establish the so called structure formula in full generality. Finally we give a stochastic construction of partial balayage.

1 - 8 of 8
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