Browsing by Author "Musso, Monica"

Now showing 1 - 20 of 26
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    Beyond the Trudinger-Moser supremum
    (2012) del Pino, Manuel; Musso, Monica; Ruf, Bernhard
    Let Omega be a bounded, smooth domain in R-2. We consider the functional
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    Bistable Boundary Reactions in Two Dimensions
    (2011) Davila, Juan; del Pino, Manuel; Musso, Monica
    In a bounded domain Omega subset of R(2) with smooth boundary we consider the problem Delta U =0 in Omega, du/dv = i/epsilon f(u) on d Omega
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    Boundary singularities for weak solutions of semilinear elliptic problems
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2007) del Pino, Manuel; Musso, Monica; Pacard, Frank
    Let Omega be a bounded domain in R-N, N >= 2, with smooth boundary partial derivative Omega. We construct positive weak solutions of the problem Delta u + u(p) = 0 in Omega, which vanish in a suitable trace sense on partial derivative Omega, but which are singular at prescribed isolated points if p is equal or slightly above N+1/N-1. Similar constructions are carried out for solutions which are singular at any given embedded submanifold of partial derivative Omega of dimension k epsilon [0, N -2], if p equals or it is slightly above N-k-1/N-k-1, and even on countable families of these objects, dense on a given closed set. The role of the exponent N+1/N-1 (first discovered by Brezis and Turner [H. Brezis, R. Turner, N-1 On a class of superlinear elliptic problems, Comm. Partial Differential Equations 2 (1977) 601-614]) for boundary regularity, parallels that of N/N-2 for interior singularities. (c) 2007 Elsevier Inc. All rights reserved.
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    Bubbling solutions for an elliptic equation with exponential Neumann data in R2
    (2014) Deng, Shengbing; Musso, Monica
    Let Omega be a bounded domain in R-2 with smooth boundary; we study the following Neumann problem
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    Concentrating solutions for a planar elliptic problem involving nonlinearities with large exponent
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2006) Esposito, Pierpaolo; Musso, Monica; Pistoia, Angela
    We consider the boundary value problem Delta u + u(P) = 0 in a bounded, smooth domain Omega in R-2 with homogeneous Dirichlet boundary condition and p a large exponent. We find topological conditions on Omega which ensure the existence of a positive solution up concentrating at exactly m points as p -> infinity. In particular, for a nonsimply connected domain such a solution exists for any given m >= 1. (c) 2006 Elsevier Inc. All rights reserved.
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    Fast and slow decay solutions for supercritical elliptic problems in exterior domains
    (2008) Davila, Juan; del Pino, Manuel; Musso, Monica; Wei, Juncheng
    We consider the elliptic problem Delta u + u(p) = 0, u > 0 in an exterior domain, Omega = R(N)\D under zero Dirichlet and vanishing conditions, where D is smooth and bounded in R(N), N >= 3, and p is supercritical, namely p > N+2/N-2. We prove that this problem has infinitely many solutions with slow decay O(vertical bar x vertical bar(-2/p-1)) at infinity. In addition, a solution with fast decay O(vertical bar x vertical bar(2- N)) exists if p is close enough from above to the critical exponent.
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    Interior bubbling solutions for the critical Lin-Ni-Takagi problem in dimension 3
    (2019) del Pino, Manuel; Musso, Monica; Roman, Carlos; Wei, Juncheng
    We consider the problem of finding positive solutions of the problem u -.u + u5 = 0 in a bounded, smooth domain in R3, under zero Neumann boundary conditions. Here. is a positive number. We analyze the role of Green's function of - +. in the presence of solutions exhibiting single bubbling behavior at one point of the domain when. is regarded as a parameter. As a special case of our results, we find and characterize a positive value.* such that if. -. * > 0 is sufficiently small, then this problem is solvable by a solution u. which blows-up by bubbling at a certain interior point of lambda down arrow lambda(*).
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    Large energy entire solutions for the Yamabe equation
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2011) del Pino, Manuel; Musso, Monica; Pacard, Frank; Pistoia, Angela
    We consider the Yamabe equation Delta u + n(n-2_/4 vertical bar u vertical bar 4/n-2 u = 0 in R(n), n >= 3. Let k >= 1 and xi(k)(j) = (e(2j pi u/k), 0) is an element of R(n) = C x R(n-2). For all large k we find a solution of the form u(k)(x)= u(x) - Sigma(k)(j=1) mu(k) (-n-2/2) U X (mu(-1)(k) (x - xi(j)) +o(1), where U(x) = (2/1+vertical bar x vertical bar(2)) (n-2/2), mu(k) = c(n)/k(2) for n >= 4, mu k = c/k(2)(logk)(2) for n =3 and o(1) -> 0 uniformly as k -> +infinity. (C) 2011 Elsevier Inc. All rights reserved.
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    Morse index and bifurcation of p-geodesics on semi Riemannian manifolds
    (EDP SCIENCES S A, 2007) Musso, Monica; Pejsachowicz, Jacobo; Portaluri, Alessandro
    Given a one-parameter family {g(lambda) :lambda is an element of [ a, b]} of semi Riemannian metrics on an n-dimensional manifold M, a family of time-dependent potentials {V-lambda: lambda is an element of [a, b]} and a family {sigma(lambda): lambda is an element of [ a, b]} of trajectories connecting two points of the mechanical system defined by ( g(lambda),V-lambda), we show that there are trajectories bifurcating from the trivial branch s. if the generalized Morse indices mu(sigma(a)) and mu(sigma(a)) are different. If the data are analytic we obtain estimates for the number of bifurcation points on the branch and, in particular, for the number of strictly conjugate points along a trajectory using an explicit computation of the Morse index in the case of locally symmetric spaces and a comparison principle of Morse Schrodenberg type.
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    Multipeak solutions to the Bahri-Coron problem in domains with a shrinking hole
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2009) Clapp, Monica; Musso, Monica; Pistoia, Angela
    We construct positive and sign changing multipeak solutions to the Pure critical exponent problem in a bounded domain with a shrinking hole, having a peak which concentrates at some point inside the shrinking hole (i.e. outside the domain) and one or more peaks which concentrate at interior points of the domain. These are, to Our knowledge, the first multipeak solutions in a domain with a single small hole. (C) 2008 Elsevier Inc. All rights reserved.
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    New solutions for Trudinger-Moser critical equations in R-2
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2010) del Pino, Manuel; Musso, Monica; Ruf, Bernhard
    Let Omega be a bounded, smooth domain in R-2. We consider critical points of the Trudinger-Moser type functional J(lambda) (u) = 1/2 integral(Omega)vertical bar del u vertical bar(2) - lambda/2 integral(Omega)e(u2) in H-0(1)(Omega), namely solutions of the boundary value problem Delta u + lambda ue(u2) = 0 with homogeneous Dirichlet boundary conditions, where lambda > 0 is a small parameter. Given k >= 1 we find conditions under which there exists a solution u(lambda) which blows up at exactly k points in Omega as lambda -> 0 and J(lambda)(u(lambda)) -> 2k pi. We find that at least one such solution always exists if k = 2 and Omega is not simply connected. If Omega has d >= 1 holes, in addition d + 1 bubbling solutions with k = 1 exist. These results are existence counterparts of one by Druet in [O. Druet, Multibump analysis in dimension 2: Quantification of blow-up levels, Duke Math. J. 132 (2) (2006) 217-269] which classifies asymptotic bounded energy levels of blow-up solutions for a class of nonlinearities of critical exponential growth, including this one as a prototype case. (C) 2009 Elsevier Inc. All rights reserved.
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    NONDEGENERACY OF ENTIRE SOLUTIONS OF A SINGULAR LIOUVILLLE EQUATION
    (AMER MATHEMATICAL SOC, 2012) del Pino, Manuel; Esposito, Pierpaolo; Musso, Monica
    We establish nondegeneracy of the explicit family of finite mass solutions of the Liouvillle equation with a singular source of integer multiplicity, in the sense that all bounded elements in the kernel of the linearization correspond to variations along the parameters of the family.
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    Nonradial Solutions to Critical Elliptic Equations of Caffarelli-Kohn-Nirenberg Type
    (OXFORD UNIV PRESS, 2012) Musso, Monica; Wei, Juncheng
    We build an unbounded sequence of nonradial solutions for
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    On spikes concentrating on line-segments to a semilinear Neumann problem
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2011) Ao, Weiwei; Musso, Monica; Wei, Juncheng
    We consider the following singularly perturbed Neumann problem
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    On the existence and profile of nodal solutions for a two-dimensional elliptic problem with large exponent in nonlinearity
    (WILEY, 2007) Esposito, Pierpaolo; Musso, Monica; Pistoia, Angela
    We study the existence of nodal solutions to the boundary value problem -Delta u = \u\(p-1)u in a bounded, smooth domain Omega in R-2, with homogeneous Dirichlet boundary condition, when p is a large exponent. We prove that, for p large enough, there exist at least two pairs of solutions which change sign exactly once and whose nodal lines intersect the boundary of Omega.
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    Sign changing solutions to a Bahri-Coron's problem in pierced domains
    (AMER INST MATHEMATICAL SCIENCES-AIMS, 2008) Musso, Monica; Pistoia, Angela
    We consider the problem
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    Sign changing solutions to a nonlinear elliptic problem involving the critical Sobolev exponent in pierced domains
    (GAUTHIER-VILLARS/EDITIONS ELSEVIER, 2006) Musso, Monica; Pistoia, Angela
    We consider the problem Delta u + \u\(4/n-2) u = 0 in Omega(epsilon), u = 0 on partial derivative Omega(epsilon), where Omega(epsilon) := Omega \ B (0, epsilon) and Omega is a bounded smooth domain in R(N), which contains the origin and is symmetric with respect to the origin, N >= 3 and epsilon is a positive parameter. As epsilon goes to zero, we construct sign changing solutions with multiple blow up at the origin. (C) 2006 Elsevier Masson SAS. All rights reserved.
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    Sign Changing Tower of Bubbles for an Elliptic Problem at the Critical Exponent in Pierced Non-Symmetric Domains
    (TAYLOR & FRANCIS INC, 2010) Ge, Yuxin; Musso, Monica; Pistoia, Angela
    We consider the problem [image omitted] in epsilon, u=0 on epsilon, where epsilon: =\{B(a, epsilon) B(b, epsilon)}, with a bounded smooth domain in N, N epsilon 3, ab two points in , and epsilon is a positive small parameter. As epsilon goes to zero, we construct sign changing solutions with multiple blow up both at a and at b.
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    Singular limits for the bi-Laplacian operator with exponential nonlinearity in R-4
    (GAUTHIER-VILLARS/EDITIONS ELSEVIER, 2008) Clapp, Monica; Munoz, Claudio; Musso, Monica
    Let Omega be a bounded smooth domain in R-4 such that for some integer d >= 1 its d-th singular cohomology group with coefficients in some field is not zero, then problem
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    Singular limits of a two-dimensional boundary value problem arising in corrosion modelling
    (2006) Davila, Juan; Del Pino, Manuel; Musso, Monica; Wei, Juncheng
    We consider the boundary value problem