1,721,180 research outputs found
Art Martinazzi oral history interview
No full textAn audio recording of an oral history of Art Martinazzi. There is a transcript of this interview
Toni Martinazzi recollections about Annie Pearl Comb Shaw Remillard
Get PDFA written recollection by Toni Martinazzi on the life of Annie Pearl Comb Shaw Remillard
Toni Martinazzi letter to Jack Broome on some historical objects from her family
Get PDFA letter from Toni Martinazzi to Jack Broome regarding the history of some items she donated to the Tualatin Historical Society
Blow-up behaviour of a fractional Adams-Moser-Trudinger type inequality in odd dimension
Get PDFGiven a smoothly bounded domain \Omega\Subset\mathbb{R}^n with n\ge 1 odd, we study the blow-up of bounded sequences (u_k)\subset H^\frac{n}{2}_{00}(\Omega) of solutions to the non-local equation
(-\Delta)^\frac n2 u_k=\lambda_k u_ke^{\frac n2 u_k^2}\quad \text{in
}\Omega,
where \lambda_k\to\lambda_\infty \in [0,\infty), and H^{\frac n2}_{00}(\Omega) denotes the Lions-Magenes spaces of functions u\in L^2(\mathbb{R}^n) which are supported in \Omega and with (-\Delta)^\frac{n}{4}u\in L^2(\mathbb{R}^n). Extending previous works of Druet, Robert-Struwe and the second author, we show that if the sequence (u_k) is not bounded in L^\infty(\Omega), a suitably rescaled subsequence \eta_k converges to the function \eta_0(x)=\log\left(\frac{2}{1+|x|^2}\right), which solves the prescribed non-local Q-curvature equation
(-\Delta)^\frac n2 \eta
=(n-1)!e^{n\eta}\quad \text{in }\mathbb{R}^n
recently studied by Da Lio-Martinazzi-Rivi\`ere when n=1, Jin-Maalaoui-Martinazzi-Xiong when n=3, and Hyder when n\ge 5 is odd. We infer that blow-up can occur only if \Lambda:=\limsup_{k\to \infty}\|(-\Delta)^\frac n4 u_k\|_{L^2}^2\ge \Lambda_1:= (n-1)!|S^n|
Conformal metrics on R-2m with constant Q-curvature Luca Martinazzi
No full textWe study the conformal metrics on R-2m with constant Q-curvature Q is an element of R having finite volume, particularly in the case Q <= 0. We show that when Q < 0 such metrics exist in R-2m if and only if m > 1. Moreover, we study their asymptotic behavior at infinity, in analogy with the case Q > 0, which we treated in a recent paper. When Q D 0, we show that such metrics have the form e(2p) g(R2m), where p is a polynomial such that 2 <= deg p <= 2 m 2 and sup(R2m) p < infinity. In dimension 4, such metrics correspond to the polynomials p of degree 2 with lim(|x|->infinity) p(x) = -infinity
Caderno, diversas matérias, Martinazzi, 4º ano, SP, 1941.
No full textCaderno em brochura, em bom estado, parte do acervo pessoal de D. Margarida Martinazzi (nome de solteira), mãe da Profa.Dra.Regina Grando, presidente da SBEM (2016-2019). O curso primário estava vinculado ao Grupo Escolar Dona Castorina Cavalheiro, criado em 1925, situado a Rua Prefeito Passos, 95 Vl. Itapura, Campinas, SP, CEP 13012-100. Atualmente denominada como Escola Estadual Dona Castorina Cavalheiro. De acordo com o registro da capa (indica-se a idade de 10 anos)e a data de nascimento de D. Margarida, conclui-se que este caderno foi escrito em 1941.Caderno com diversas matérias para o ensino primário, 4º ano. Há atividades de aritmética, geometria, sistemas de medidas, etc. O caderno foi escrito pela própria aluna como cópia de lousa. O mesmo Não era deixado com a professora e sim levado todos os dias para casa
Clyde C. Young oral history transcript
Get PDFA very brief transcript of an oral history interview of Clyde C. Young. Clyde was interviewed by Toni Martinazzi on June 10, 1989 as part of her research on her family's history. The interview concerns the family of Clyde's wife, Catherine Teresa Martinazzi Young. Topics include their timber and farm property in Tualatin
Quantization for the prescribed Q-curvature equation on open domains
No full textWe discuss compactness, blow-up and quantization phenomena for the prescribed Q-curvature equation (−Δ)muk=Vke2muk on open domains of . Under natural integral assumptions we show that when blow-up occurs, up to a subsequence
limk→∞∫Ω0Vke2mukdx=LΛ1,
where Ω0⊂⊂Ω is open and contains the blow-up points, L∈N and \Lambda_1:=(2m-1)!\vol(S^{2m}) is the total Q-curvature of the round sphere S2m. Moreover, under suitable assumptions, the blow-up points are isolated. We do not assume that V is positive
Concentration–compactness phenomena in the higher order Liouville's equation
No full textAbstractWe investigate different concentration–compactness and blow-up phenomena related to the Q-curvature in arbitrary even dimension. We first treat the case of an open domain in R2m, then that of a closed manifold and, finally, the particular case of the sphere S2m. In all cases we allow the sign of the Q-curvature to vary, and show that in the case of a closed manifold, contrary to the case of open domains in R2m, blow-up phenomena can occur only at points of positive Q-curvature. As a consequence, on a locally conformally flat manifold of non-positive Euler characteristic we always have compactness
Fractional Adams–Moser–Trudinger type inequalities
Get PDFExtending several works, we prove a general Adams Moser Trudinger type inequality for the embedding of Bessel-potential spaces (r2) into Orlicz spaces for an arbitrary domain,r2 with finite measure. In particular we prove
sup (u is an element of Hn/p,p (Omega), parallel to(-Delta)n/2p u parallel to LP(Omega)<= 1) integral Omega (E alpha n,p broken vertical bar u broken vertical bar p/p-1dx <= Cn,p broken vertical bar Omega broken vertical bar,)
for a positive constant amp whose sharpness we also prove. We further extend this result to the case of Lorentz-spaces (i.e. (-Delta) u is an element of L-(P,L-q)). The proofs are simple, as they use Green functions for fractional Laplace operators and suitable cut-off procedures to reduce the fractional results to the sharp estimate on the Riesz potential proven by Adams and its generalization proven by Xiao and Zhai. We also discuss an application to the problem of prescribing the Q-curvature and some open problems
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