51 research outputs found
WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR p-EVOLUTION SYSTEMS OF PSEUDO-DIFFERENTIAL OPERATORS
We study p-evolution pseudo-differential systems of the first order with coefficients in (t,x) and real characteristics. We find sufficient conditions for the well-posedness of
the Cauchy problem in H∞. These conditions involve the behavior as x → ∞ of the coefficients, requiring some decay estimates to be satisfied
Semilinear p-evolution equations in Sobolev spaces
We prove local in time well-posedness in Sobolev spaces of the Cauchy problem
for semi-linear p-evolution equations of the first order with real principal
part, but complex valued coefficients for the lower order terms, assuming decay
conditions on the imaginary parts as |x| goes to infinity
Random-field Solutions to Linear Hyperbolic Stochastic Partial Differential Equations with Variable Coefficients
In this article we show the existence of a random-field solution to linear
stochastic partial differential equations whose partial differential operator
is hyperbolic and has variable coefficients that may depend on the temporal and
spatial argument. The main tools for this, pseudo-differential and Fourier
integral operators, come from microlocal analysis. The equations that we treat
are second-order and higher-order strictly hyperbolic, and second-order weakly
hyperbolic with uniformly bounded coefficients in space. For the latter one we
show that a stronger assumption on the correlation measure of the random noise
might be needed. Moreover, we show that the well-known case of the stochastic
wave equation can be embedded into the theory presented in this article.Comment: 40 pages, final version, Stochastic Processes and their Applications
(2017
The Cauchy problem for finitely degenerate hyperbolic equations with polynomial coefficients
We consider hyperbolic Cauchy problems with characteristics of variable multiplicity and coefficients of polynomial growth in the space variables; we focus on second order equations and admit finite order intersections between the characteristics. We obtain well posedness results in S(R^n), S'(R^n) by imposing suitable Levi conditions on the lower order terms. By an energy estimate in weighted Sobolev spaces we show that regularity and behavior at infinity of the solution are different from the ones of the data
On the Cauchy problem for -evolution equations with variable coefficients: a necessary condition for Gevrey well-posedness
In this paper we consider a class of -evolution equations of arbitrary
order with variable coefficients depending on time and space variables .
We prove necessary conditions on the decay rates of the coefficients for the
well-posedness of the related Cauchy problem in Gevrey spaces.Comment: 20 page
Colorectal Cancer Stage at Diagnosis Before vs During the COVID-19 Pandemic in Italy
IMPORTANCE Delays in screening programs and the reluctance of patients to seek medical
attention because of the outbreak of SARS-CoV-2 could be associated with the risk of more advanced
colorectal cancers at diagnosis.
OBJECTIVE To evaluate whether the SARS-CoV-2 pandemic was associated with more advanced
oncologic stage and change in clinical presentation for patients with colorectal cancer.
DESIGN, SETTING, AND PARTICIPANTS This retrospective, multicenter cohort study included all
17 938 adult patients who underwent surgery for colorectal cancer from March 1, 2020, to December
31, 2021 (pandemic period), and from January 1, 2018, to February 29, 2020 (prepandemic period),
in 81 participating centers in Italy, including tertiary centers and community hospitals. Follow-up was
30 days from surgery.
EXPOSURES Any type of surgical procedure for colorectal cancer, including explorative surgery,
palliative procedures, and atypical or segmental resections.
MAIN OUTCOMES AND MEASURES The primary outcome was advanced stage of colorectal cancer
at diagnosis. Secondary outcomes were distant metastasis, T4 stage, aggressive biology (defined as
cancer with at least 1 of the following characteristics: signet ring cells, mucinous tumor, budding,
lymphovascular invasion, perineural invasion, and lymphangitis), stenotic lesion, emergency surgery,
and palliative surgery. The independent association between the pandemic period and the outcomes
was assessed using multivariate random-effects logistic regression, with hospital as the cluster
variable.
RESULTS A total of 17 938 patients (10 007 men [55.8%]; mean [SD] age, 70.6 [12.2] years)
underwent surgery for colorectal cancer: 7796 (43.5%) during the pandemic period and 10 142
(56.5%) during the prepandemic period. Logistic regression indicated that the pandemic period was
significantly associated with an increased rate of advanced-stage colorectal cancer (odds ratio [OR],
1.07; 95%CI, 1.01-1.13; P = .03), aggressive biology (OR, 1.32; 95%CI, 1.15-1.53; P < .001), and stenotic
lesions (OR, 1.15; 95%CI, 1.01-1.31; P = .03).
CONCLUSIONS AND RELEVANCE This cohort study suggests a significant association between the
SARS-CoV-2 pandemic and the risk of a more advanced oncologic stage at diagnosis among patients
undergoing surgery for colorectal cancer and might indicate a potential reduction of survival for
these patients
Analisi microlocale ed applicazioni: PDEs stocastiche e di evoluzione, analisi tempo- frequenza, varietà
Progetto Gnampa 202
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