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• 1.
Dublin Institute of Technology.
Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry2012In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 75, no 1, p. 384-404Article in journal (Refereed)

We establish the existence of infinitely many distinct solutions to the multi-configurative Hartree-Fock type equations for N-electron Coulomb systems with quasi-relativistic kinetic energy root-alpha(-2)Delta(xn) + alpha(-4) - alpha(-2) for the nth electron. Finitely many of the solutions are interpreted as excited states of the molecule. Moreover, we prove the existence of a ground state. The results are valid under the hypotheses that the total charge Z(tot) of K nuclei is greater than N - 1 and that Z(tot) is smaller than a critical charge Z(c). The proofs are based on a new application of the Lions-Fang-Ghoussoub critical point approach to nonminimal solutions on a complete analytic Hilbert-Riemann manifold, in combination with density operator techniques. (C) 2011 Elsevier Ltd. All rights reserved.

• 2.
Dublin Institute of Technology.
Dublin Institute of Technology.
Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry (vol 75, pg 384, 2012)2012In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 75, no 6, p. 3274-3275Article in journal (Refereed)
• 3. Avelin, Benny
Optimal doubling, Reifenberg flatness and operators of p-Laplace type2011In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, no 17, p. 5943-5955Article in journal (Refereed)

In this paper we consider operators of p-Laplace type of the form ∇·A(x,∇u) = 0. ConcerningA we assume, for p ∈ (1,∞) fixed, an appropriate ellipticity type condition, H¨older continuityin x and that A(x, ) = ||p−1A(x, /||) whenever x ∈ Rn and ∈ Rn \ {0}. Let  ⊂ Rn be abounded domain, let D be a compact subset of . We say that ˆu = ˆup,D, is the A-capacitaryfunction for D in  if ˆu ≡ 1 on D, ˆu ≡ 0 on @ in the sense of W1,p0 () and ∇·A(x,∇ˆu) = 0 in \D in the weak sense. We extend ˆu to Rn \  by putting ˆu ≡ 0 on Rn \ . Then there existsa unique finite positive Borel measure ˆμ on Rn, with support in @, such thatZ hA(x,∇ˆu),∇i dx = −Z dˆμ whenever ∈ C∞0 (Rn \ D).In this paper we prove that if  is Reifenberg flat with vanishing constant, thenlimr→0infw∈∂ˆμ(B(w, r))ˆμ(B(w, r))= limr→0supw∈∂ˆμ(B(w, r))ˆμ(B(w, r))= n−1,for every , 0 < ≤ 1. In particular, we prove that ˆμ is an asymptotically optimal doublingmeasure on @.

• 4.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Wolff-Potential Estimates and Doubling of Subelliptic p-harmonic measures2013In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 85, p. 149-159Article in journal (Refereed)

Let be a system of C vector fields in Rn satisfying Hörmander’s finite rank condition and let Ω be a non-tangentially accessible domain with respect to the Carnot–Carathéodory distance d induced by X. We prove the doubling property of certain boundary measures associated to non-negative solutions, which vanish on a portion of Ω, to the equation

Given p, 1<p<, fixed, we impose conditions on the function A=(A1,…,Am):Rn×RmRm, which imply that the equation is a quasi-linear partial differential equation of p-Laplace type structured on vector fields satisfying the classical Hörmander condition. In the case p=2 and for linear equations, our result coincides with the doubling property of associated elliptic measures. To prove our result we establish, and this is of independent interest, a Wolff potential estimate for subelliptic equations of p-Laplace type.

• 5. Babaoglu, Ceni
Department of Mathematics, Stockholm University.
Some properties of two-phase quadrature domains2011In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, no 10, p. 3386-3396Article in journal (Refereed)
• 6.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Lorentz estimates for obstacle parabolic problems2014In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 96, p. 167-188Article in journal (Refereed)

We prove that the spatial gradient of (variational) solutions to parabolic obstacle problems of p-Laplacian type enjoys the same regularity of the data and of the derivatives of the obstacle in the scale of Lorentz spaces.

• 7.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Harnack inequalities for double phase functionals2015In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 121, p. 206-222Article in journal (Refereed)

We prove a Harnack inequality for minimisers of a class of non-autonomous functionals with non-standard growth conditions. They are characterised by the fact that their energy density switches between two types of different degenerate phases.

• 8.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
Gdansk University of Technology.
Asymptotic properties of quadratic stochastic operators acting on the L1 space2015In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 114, p. 26-39Article in journal (Refereed)

Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours andthese have been introduced and studied recently in the l1 space. It turns out that inprinciple most of the results can be carried over to the L1 space. However, due to topologicalproperties of this space one has to restrict in some situations to kernel quadratic stochasticoperators. In this article we study the uniform and strong asymptotic stability of quadratic stochastic operators acting on the L1 space in terms of convergence of the associated (linear)nonhomogeneous Markov chains.

• 9.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Existence of a solution to Hartree-Fock equations with decreasing magnetic fields2008In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 69, no 7, p. 2125-2141Article in journal (Refereed)

In the presence of an external magnetic field, we prove existence of a ground state within the Hartree-Fock theory of atoms and molecules. The ground state exists provided the magnetic field decreases at infinity and the total charge Z of K nuclei exceeds N - 1, where N is the number of electrons. In the opposite direction, no ground state exists if N > ; 2Z + K.

• 10.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
Efficiency in the adaptive solution of inviscid compressible flow problems2001In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 47, p. 3467-3478Article in journal (Refereed)
• 11. Medeiros, Everaldo
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
Multiplicity results for problems involving the Hardy-Sobolev operator via Morse theory2010In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 72, no 5, p. 2170-2177Article in journal (Refereed)

We establish some multiplicity results for a class of boundary value problems involving the Hardy-Sobolev operator using Morse theory. (C) 2009 Elsevier Ltd. All rights reserved.

• 12.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Extension properties and boundary estimates for a fractional heat operator2016In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 140, p. 29-37Article in journal (Refereed)

The square root of the heat operator $\sqrt{\partial_t-\Delta}$, can be realized as the Dirichlet to Neumann map of the heat extension of data on $\mathbb R^{n+1}$ to $\mathbb R^{n+2}_+$. In this note we obtain similar characterizations for general fractional powers of the heat operator, $(\partial_t-\Delta)^s$, $s\in (0,1)$. Using the characterizations we derive properties and boundary estimates for parabolic integro-differential equations from purely local arguments in the extension problem.

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