0 one can find a simple 1-dimensional constant coefficient linear equation whose solution at the boundary is not α-Hölder continuous.We obtain a positive counterpart of this: under some mild regularity assumptions on the coefficients, solutions of semilinear SPDEs on C1 domains are proved to be α-Hölder continuous up to the boundary with some α>0.}, author = {Gerencser, Mate}, issn = {00911798}, journal = {Annals of Probability}, number = {2}, pages = {804--834}, publisher = {Institute of Mathematical Statistics}, title = {{Boundary regularity of stochastic PDEs}}, doi = {10.1214/18-AOP1272}, volume = {47}, year = {2019}, } @article{301, abstract = {A representation formula for solutions of stochastic partial differential equations with Dirichlet boundary conditions is proved. The scope of our setting is wide enough to cover the general situation when the backward characteristics that appear in the usual formulation are not even defined in the Itô sense.}, author = {Gerencser, Mate and Gyöngy, István}, journal = {Stochastic Processes and their Applications}, number = {3}, pages = {995--1012}, publisher = {Elsevier}, title = {{A Feynman–Kac formula for stochastic Dirichlet problems}}, doi = {10.1016/j.spa.2018.04.003}, volume = {129}, year = {2019}, } @article{65, abstract = {We provide an entropy formulation for porous medium-type equations with a stochastic, non-linear, spatially inhomogeneous forcing. Well-posedness and L1-contraction is obtained in the class of entropy solutions. Our scope allows for porous medium operators Δ(|u|m−1u) for all m∈(1,∞), and Hölder continuous diffusion nonlinearity with exponent 1/2.}, author = {Dareiotis, Konstantinos and Gerencser, Mate and Gess, Benjamin}, journal = {Journal of Differential Equations}, number = {6}, pages = {3732--3763}, publisher = {Elsevier}, title = {{Entropy solutions for stochastic porous media equations}}, doi = {10.1016/j.jde.2018.09.012}, volume = {266}, year = {2019}, } @article{319, abstract = {We study spaces of modelled distributions with singular behaviour near the boundary of a domain that, in the context of the theory of regularity structures, allow one to give robust solution theories for singular stochastic PDEs with boundary conditions. The calculus of modelled distributions established in Hairer (Invent Math 198(2):269–504, 2014. https://doi.org/10.1007/s00222-014-0505-4) is extended to this setting. We formulate and solve fixed point problems in these spaces with a class of kernels that is sufficiently large to cover in particular the Dirichlet and Neumann heat kernels. These results are then used to provide solution theories for the KPZ equation with Dirichlet and Neumann boundary conditions and for the 2D generalised parabolic Anderson model with Dirichlet boundary conditions. In the case of the KPZ equation with Neumann boundary conditions, we show that, depending on the class of mollifiers one considers, a “boundary renormalisation” takes place. In other words, there are situations in which a certain boundary condition is applied to an approximation to the KPZ equation, but the limiting process is the Hopf–Cole solution to the KPZ equation with a different boundary condition.}, author = {Gerencser, Mate and Hairer, Martin}, issn = {14322064}, journal = {Probability Theory and Related Fields}, number = {3-4}, pages = {697–758}, publisher = {Springer}, title = {{Singular SPDEs in domains with boundaries}}, doi = {10.1007/s00440-018-0841-1}, volume = {173}, year = {2019}, } @unpublished{75, abstract = {We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and perimeters for any integer m≥2; this result was previously known for prime powers m=pk. We also give a higher-dimensional generalization.}, author = {Akopyan, Arseniy and Avvakumov, Sergey and Karasev, Roman}, pages = {11}, publisher = {arXiv}, title = {{Convex fair partitions into arbitrary number of pieces}}, year = {2018}, } @article{556, abstract = {We investigate the free boundary Schur process, a variant of the Schur process introduced by Okounkov and Reshetikhin, where we allow the first and the last partitions to be arbitrary (instead of empty in the original setting). The pfaffian Schur process, previously studied by several authors, is recovered when just one of the boundary partitions is left free. We compute the correlation functions of the process in all generality via the free fermion formalism, which we extend with the thorough treatment of “free boundary states.” For the case of one free boundary, our approach yields a new proof that the process is pfaffian. For the case of two free boundaries, we find that the process is not pfaffian, but a closely related process is. We also study three different applications of the Schur process with one free boundary: fluctuations of symmetrized last passage percolation models, limit shapes and processes for symmetric plane partitions and for plane overpartitions.}, author = {Betea, Dan and Bouttier, Jeremie and Nejjar, Peter and Vuletic, Mirjana}, issn = {14240637}, journal = {Annales Henri Poincare}, number = {12}, pages = {3663--3742}, publisher = {Fakultät für Mathematik Universität Wien}, title = {{The free boundary Schur process and applications I}}, doi = {10.1007/s00023-018-0723-1}, volume = {19}, year = {2018}, }