1,721,044 research outputs found
On the Haim Brezis pioneering contributions on the location of free boundaries
No full text5th European Conference on Elliptic and Parabolic Problems -A Special Tribute to the Work of Haim Brezis. Gaeta. 2004DGISGPI (Spain)ECDepto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasTRUEpu
Current research in nonlinear analysis: in honor of Haim Brezis and Louis Nirenberg
No full textCurrent research and applications in nonlinear analysis influenced by Haim Brezis and Louis Nirenberg are presented in this book by leading mathematicians. Each contribution aims to broaden reader’s understanding of theories, methods, and techniques utilized to solve significant problems. Topics include: Sobolev Spaces Maximal monotone operators A theorem of Brezis-Nirenberg Operator-norm convergence of the Trotter product formula Elliptic operators with infinitely many variables Pseudo-and quasiconvexities for nonsmooth function Anisotropic surface measures Eulerian and Lagrangian variables Multiple periodic solutions of Lagrangian systems Porous medium equation Nondiscrete Lassonde-Revalski principle Graduate students and researchers in mathematics, physics, engineering, and economics will find this book a useful reference for new techniques and research areas. Haim Brezis and Louis Nirenberg’s fundamental research in nonlinear functional analysis and nonlinear partial differential equations along with their years of teaching and training students have had a notable impact in the field
Explicit 2D ∞-harmonic maps whose interfaces have junctions and corners
Full text linkGiven a map u:Ω⊆Rn→RN, the ∞-Laplacian is the system:(1)δ∞u:=(Du⊗Du+|Du|2[Du]⊥⊗I):D2u=0 and arises as the "Euler-Lagrange PDE" of the supremal functional E∞(u,Ω)={norm of matrix}Du{norm of matrix}L∞(Ω). (1) is the model PDE of the vector-valued Calculus of Variations in L∞ and first appeared in the author's recent work [10-14]. Solutions to (1) present a natural phase separation with qualitatively different behaviour on each phase. Moreover, on the interfaces the coefficients of (1) are discontinuous. Herein we construct new explicit smooth solutions for n=N=2, for which the interfaces have triple junctions and non-smooth corners. The high complexity of these solutions provides further understanding of the PDE (1) and limits what might be true in future regularity considerations of the interfaces. © 2013 Académie des sciences
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Counterexamples in calculus of variations in L∞ through the vectorial Eikonal equation
Full text linkWe show that, for any regular bounded domain Ω⊆Rn, n=2,3, there exist infinitely many global diffeomorphisms equal to the identity on ∂Ω that solve the Eikonal equation. We also provide explicit examples of such maps on annular domains. This implies that the ∞-Laplace system arising in vectorial calculus of variations in L∞ does not suffice to characterise either limits of p-Harmonic maps as p→∞ or absolute minimisers in the sense of Aronsson
Some geometric and spectral aspects of restriction problems
Full text linkThis texts commemorates the memory of Haim Brezis and explores some aspects of the restriction problem, particularly its connections to spectral and geometric analysis. Our choice of subject is motivated by Brezis' significant contributions to various domains related to this problem, including harmonic analysis, partial differential equations, spectral theory, representation theory, number theory, and many others
Some geometric and spectral aspects of restriction problems
Full text linkThis texts commemorates the memory of Haim Brezis and explores some aspects of the restriction problem, particularly its connections to spectral and geometric analysis. Our choice of subject is motivated by Brezis' significant contributions to various domains related to this problem, including harmonic analysis, partial differential equations, spectral theory, representation theory, number theory, and many others
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