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Sökning: LAR1:ltu

  • Resultat 44521-44530 av 52875
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44521.
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44522.
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44523.
  • Strömberg, Thomas (författare)
  • A counterexample to uniqueness of generalized characteristics in Hamilton-Jacobi theory
  • 2011
  • Ingår i: Nonlinear Analysis. - : Elsevier BV. - 0362-546X .- 1873-5215. ; 74:7, s. 2758-2762
  • Tidskriftsartikel (refereegranskat)abstract
    • The notion of generalized characteristics plays a pivotal role in the study of propagation of singularities for Hamilton{Jacobi equations. This note gives an example of nonuniqueness of forward generalized characteristics emanating from a given point.
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44524.
  • Strömberg, Thomas (författare)
  • A new proof of indefinite propagation of singularities for a Hamilton-Jacobi equation
  • 2016
  • Ingår i: Journal of evolution equations (Printed ed.). - : Springer Science and Business Media LLC. - 1424-3199 .- 1424-3202. ; 16:4, s. 895-903
  • Tidskriftsartikel (refereegranskat)abstract
    • We study propagation of singularities for the Hamilton–Jacobi equation S t +H(∇S)=0,(t,x)∈(0,T)×R n , St+H(∇S)=0,(t,x)∈(0,T)×Rn,where H(p)=12 ⟨p,Ap⟩ H(p)=12⟨p,Ap⟩ is a positive definite quadratic form. Each viscosity solution S S is semiconcave, and it is known that its singularities move along generalized characteristics. We give a new proof of the recent result by Cannarsa et al. (Discrete Contin Dyn Syst 35:4225–4239, 2015), namely that the singularities propagate along generalized characteristics indefinitely forward in time. 
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44525.
  • Strömberg, Thomas (författare)
  • A note on the differentiability of conjugate functions
  • 2009
  • Ingår i: Archiv der Mathematik. - : Springer Science and Business Media LLC. - 0003-889X .- 1420-8938. ; 93:5, s. 481-485
  • Tidskriftsartikel (refereegranskat)abstract
    • For a proper, lower semicontinuous and convex function f with Legendre-Fenchel conjugate f *, it is well-known that differentiability properties of f * are equivalent to strict convexity properties of f. In this note a result of this kind is obtained without a convexity assumption on f.
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44526.
  • Strömberg, Thomas (författare)
  • A study of the operation of infimal convolution
  • 1994
  • Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
    • This thesis consists of five papers (A-E), which examine the operation of infimal convolution and discuss its close connections to unilateral analysis, convex analysis, inequalities, approximation, and optimization. In particular, we attempt to provide a detailed investigation for both the convex and the non-convex case, including several examples. Paper (A) is both a survey of and a self-contained introduction to the operation of infimal convolution. In particular, we discuss the infimal value and minimizers of an infimal convolute, infimal convolution on subadditive functions, sufficient conditions for semicontinuity or continuity of an infimal convolute, "exactness," regularizing effects, continuity of the operation of infimal convolution, and approximation methods based on infimal convolution. A Young-type inequality, closely connected to the operation of infimal convolution, is studied in paper (B). The main results obtained are an equivalence theorem and a representation formula. In paper (C) we consider coercive, convex, proper, and lower sernicontinuous functions on a reflexive Banach space. For the infimal convolution of such functions we establish, in particular, different formulae. Moreover, we demonstrate the possibility of using the formulae obtained for solving special types of Hamilton-Jacobi equations. Furthermore, the operation of infimal convolution is interpreted from a physical viewpoint. Paper (D) presents properties of infimal convolution of functions that are uniformly continuous on bounded sets. In particular, we present regularization procedures by means of infimal convolution. The role of growth conditions on the functions under consideration is essential. Finally, in paper (E) we study semicontinuity, continuity, and differentiability of the infimal convolute of two convex functions. Moreover, under certain geometric conditions, the classical Moreau-Yosida approximation process is, roughly speaking, extended to the non-convex case.
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44527.
  • Strömberg, Thomas (författare)
  • A system of the Hamilton-Jacobi and the continuity equations in the vanishing viscosity limit
  • 2011
  • Ingår i: Communications on Pure and Applied Analysis. - : American Institute of Mathematical Sciences (AIMS). - 1534-0392 .- 1553-5258. ; 10:2, s. 479-506
  • Tidskriftsartikel (refereegranskat)abstract
    • We study the following system of the viscous Hamilton-Jacobi and the continuity equations in the limit as epsilon down arrow 0: S-t(epsilon) + 1/2 vertical bar DS epsilon vertical bar(2) + V(x) - epsilon Delta S-epsilon = 0 in Q(T), S-epsilon(0, x) = S-0(x) in R-n; rho(epsilon)(t) + div(rho(epsilon) DS epsilon) = 0 in Q(T), rho(epsilon)(0, x) = rho(0)(x) in R-n. Here Q(T) = (0, T] x R-n. The potential V and the initial function S-0 are allowed to grow quadratically while rho(0) is a Borel measure. The paper justifies and describes the vanishing viscosity transition to the corresponding inviscid system. The notion of weak solution employed for the inviscid system is that of a viscosity-measure solution (S, rho).
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44528.
  • Strömberg, Thomas (författare)
  • An operation connected to a Young-type inequality
  • 1992
  • Ingår i: Mathematische Nachrichten. - : Wiley. - 0025-584X .- 1522-2616. ; 159, s. 227-243
  • Tidskriftsartikel (refereegranskat)abstract
    • Given two φ-functions F and G we consider the largest φ-function H = F ⊕ G such that the Young-type inequality H(xy) ⩽ F(x) + G(y) holds for all x, y > 0. We prove an equivalence theorem for F ⊕ G with the best constants and, for the special case when F and G are log-convex and satisfy a certain growth condition, a representation formula for F G. Moreover, further properties and examples are presented and the relations to similar results are discussed.
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44529.
  • Strömberg, Thomas (författare)
  • Duality between Frechet differentiability and strong convexity
  • 2011
  • Ingår i: Positivity (Dordrecht). - : Springer Science and Business Media LLC. - 1385-1292 .- 1572-9281. ; 15:3, s. 527-536
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper revisits the duality between differentiability and strict or strong convexity under the Legendre-Fenchel transform {Mathematical expression}. Functions f defined on a Banach space X are considered. For a lower semicontinuous but not necessarily convex function f we relate essential Fréchet differentiability of the conjugate function f* to essential strong convexity of f
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44530.
  • Strömberg, Thomas, et al. (författare)
  • Excess action and broken characteristics for Hamilton-Jacobi equations
  • 2014
  • Ingår i: Nonlinear Analysis. - : Elsevier BV. - 0362-546X .- 1873-5215. ; 110, s. 113-129
  • Tidskriftsartikel (refereegranskat)abstract
    • We study propagation of singularities for Hamilton-Jacobi equations S t+H(t,x,λS)=0,(t,x)∈(0,∞)×ℝn, by means of the excess Lagrangian action and a related class of characteristics. In a sense, the excess action gauges how far a curve X(t) is from being action minimizing for a given viscosity solution S(t,x) of the Hamilton-Jacobi equation. Broken characteristics are defined as curves along which the excess action grows at the slowest pace possible. In particular, we demonstrate that broken characteristics carry the singularities of the viscosity solution.
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