“…This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. …”
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“…Basic properties of zeta and L-functions are established and used to prove the prime number theorem and the Dirichlet theorem on prime numbers in arithmetic progressions. …”
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“…With the a priori estimates the existence of a [Formula: see text] solution to the obstacle problem with Dirichlet boundary value is obtained by approximation.…”
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“…The best-fitted latent Dirichlet allocation model discovered 8 different topics with a coherence score of 0.66 and a perplexity measure of –11.29. …”
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“…In addition, they tend to publish posts related to latent Dirichlet allocation topics such as relationships (Cohen d=0.105) and family and friends and mental health (Cohen d=0.10). …”
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“…Six predictors were used in the initial model and 10 additional topics from Latent Dirichlet Allocation processing were added in the enriched models. …”
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“…We also find that free finite mixtures consistently outperform empirical finite mixtures. Finally, the Dirichlet process-based mixture model tends to outperform all other approaches.…”
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“…Topics include: basic properties of harmonic functions, Poisson integrals, the Kelvin transform, spherical harmonics, harmonic Hardy spaces, harmonic Bergman spaces, the decomposition theorem, Laurent expansions, isolated singularities, and the Dirichlet problem. The new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bocher's Theorem, new exercises and proofs, as well as revisions throughout to improve the text. …”
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“…For p/in (0,1) the Q p furnish an increasing sequence of spaces, each invariant under conformal mappings of the unit disk onto itself, which interpolate between the Dirichlet space and BMOA. This monograph covers a number of important aspects in complex, functional and harmonic analysis. …”
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“…The book deals with parameter dependent problems of the form u"+*f(u)=0 on an interval with homogeneous Dirichlet or Neuman boundary conditions. These problems have a family of solution curves in the (u,*)-space. …”
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“…These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. …”
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“…The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. …”
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“…The authors prove the long time stability of KAM tori (thus quasi-periodic solutions) for nonlinear Schrödinger equation \sqrt{-1}\, u_{t}=u_{xx}-M_{\xi}u+\varepsilon|u|^2u, subject to Dirichlet boundary conditions u(t,0)=u(t,\pi)=0, where M_{\xi} is a real Fourier multiplier. …”
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“…In some cases, we express the results in terms of the Dirichlet characters. Generalizations for arbitrary m are well defined but do imply integrals and/or series summations rather involved.…”
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“…In this paper, we established a quantitative unique continuation results for a coupled heat equations, with the homogeneous Dirichlet boundary condition, on a bounded convex domain Ω of [Formula: see text] with smooth boundary ∂Ω. …”
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“…The axisymmetric time-fractional diffusion equation with mass absorption is studied in a circle under the time-harmonic Dirichlet boundary condition. The Caputo derivative of the order [Formula: see text] is used. …”
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“…A priori error estimates of the penalty method, which is used to deal with Dirichlet boundary conditions, are derived to illustrate its validity in a continuous sense. …”
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“…The author studies a class of boundary value problems for second-order elliptic differential operators which includes as particular cases the Dirichlet and Neumann problems, and proves that this class of boundary value problems provides a new example of analytic semigroups both in the Lp topology and in the topology of uniform convergence. …”
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“…The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate students in engineering, but the book may also be beneficial for lecturers, and research experts both in academia in industry.…”
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“…Characterizations of subtemperatures in terms of heat balls and modified heat balls are proved, and thermal capacity is studied in detail. The generalized Dirichlet problem on arbitrary open sets is given a treatment that reflects its distinctive nature for an equation of parabolic type. …”
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