Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 13 of 13 for “"regularity theory"”.
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Regularity theory for nonlocal equations
… is primarily concerned with proving Sobolev regularity results of Calderón-Zygmund-type for nonlinear nonlocal equations with possibly very irregular coefficients of VMO-type or even coefficients that are merely small in BMO. In particular, such coefficients might be discontinuous.<br /><br …
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Schauder Regularity Theory for Degenerate and Singular PDEs
L'abstract è presente nell'allegato / the abstract is in the attachment
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Repulsive knot energies and pseudodifferential calculus : rigorous analysis and regularity theory for O'Hara's knot energy family E (alpha), alpha in [2,3)
… proving Fréchet differentiability and $C^infty$ regularity of critical points. Using some ideas of Z.-X. He and filling major gaps in his investigation of the Möbius Energy E^(2), we furnish a rigorous proof of an even more general statement. We start with proving continuity of E^(alpha) on …
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A SYSTEM OF SUPERLINEAR ELLIPTIC EQUATIONS IN A CYLINDER
… the main technical tools: Hardy's inequality, regularity theory and maximum principle as well as the work of Brezis and Turner. They treated a general superlinear elliptic problem and obtained the existence of positive solutions for nonlinear term having an asymptotic growth $s^\gamma$ with …
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Local Regularity of the Complex Monge-Ampere Equation
… account of the current development in the local regularity theory of the complex Monge-Ampere equation through the modern fully-nonlinear PDE point of view. We have apply the modern elliptic techniques to establish new local regularity results. These includes: regularity of small perturbed …
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New and old sub-Riemannian challenges bridging analysis and geometry
… 2 PDEs over Carnot-Carathéodory structures. 3 Regularity theory for almost perimeter minimizers in Carnot groups. 4 Geometry of hypersurfaces in Heisenberg groups.
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Global Regularity for Euler Vortex Patch in Bounded Smooth Domains
… enough initially. In bounded domains, the regularity theory for patch solutions is less complete. In this thesis, I study the Euler vortex patch in a general smooth bounded domain. I prove global in time regularity by providing the upper bound of the growth on curvature of the patch …
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Non-parametric hypersurfaces of prescribed mean curvature in H n x R
… order to use techniques from geometric measure theory. The non-parametric hypersurfaces are given by graphs of height functions u over a given bounded (with respect to the hyperbolic metric) domain in $Hyp$.We solve a certain Dirichlet problem for the function u in the framework of the direct …
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On the Structure and Regularity of Stable Branched Minimal Hypersurfaces
… function with $C^{1,\alpha}$ regularity in a certain generalised sense; this settles a basic remaining open question in the study of the local structure of codimension one area minimising currents mod $p$ near points with planar tangent cones, extending the cases $p=2$ and …
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Existence and regularity of monotone solutions to a free boundary problem
… analogue of the 8-dimensional Simons cone in the theory of minimal surfaces. The minimality of the Simons cone is closely related to the existence of a complete minimal graph in dimension 9, which is not a hyperplane. The first step toward solving the analogous problem in the free boundary …
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Energy methods for nonsymmetric nonlocal operators
The goal of this thesis is to develop the regularity theory for nonlocal parabolic equations. We focus on problems driven by nonlocal operators associated with nonsymmetric bilinear forms. In contrast to the symmetric case, nonsymmetric nonlocal operators have not yet been studied systematically. …
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On regularity for integral currents - the smooth approximation of cycles
This thesis is devoted to the study of regularity properties of generalized surfaces in the Plateau problem. The first part of the thesis focuses on the regularity theory for Federer-Fleming integral currents, proving that every integral cycle can be approximated by a smooth submanifold up to a …
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Variational methods in nonsmooth analysis and quasilinear equations
A natural generalization of the classical theory of critical points is the concept of the theory of critical points for continuous functionals. A fundamental tool in this concept is the weak slope. We introduce it in the first chapter and compare it with other slopes of the literature. We show that …